{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,9,3]],"date-time":"2026-09-03T16:19:15Z","timestamp":1788452355536,"version":"build-2803163510"},"reference-count":77,"publisher":"Springer Science and Business Media LLC","issue":"1","license":[{"start":{"date-parts":[[2025,10,7]],"date-time":"2025-10-07T00:00:00Z","timestamp":1759795200000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"},{"start":{"date-parts":[[2025,10,7]],"date-time":"2025-10-07T00:00:00Z","timestamp":1759795200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"}],"funder":[{"DOI":"10.13039\/501100003593","name":"Conselho Nacional de Desenvolvimento Cient\u00edfico e Tecnol\u00f3gico","doi-asserted-by":"publisher","award":["308581\/2022-9"],"award-info":[{"award-number":["308581\/2022-9"]}],"id":[{"id":"10.13039\/501100003593","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100003593","name":"Conselho Nacional de Desenvolvimento Cient\u00edfico e Tecnol\u00f3gico","doi-asserted-by":"publisher","award":["308581\/2022-9"],"award-info":[{"award-number":["308581\/2022-9"]}],"id":[{"id":"10.13039\/501100003593","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100003593","name":"Conselho Nacional de Desenvolvimento Cient\u00edfico e Tecnol\u00f3gico","doi-asserted-by":"publisher","award":["308581\/2022-9"],"award-info":[{"award-number":["308581\/2022-9"]}],"id":[{"id":"10.13039\/501100003593","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100003593","name":"Conselho Nacional de Desenvolvimento Cient\u00edfico e Tecnol\u00f3gico","doi-asserted-by":"publisher","award":["308581\/2022-9"],"award-info":[{"award-number":["308581\/2022-9"]}],"id":[{"id":"10.13039\/501100003593","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100002322","name":"Coordena\u00e7\u00e3o de Aperfei\u00e7oamento de Pessoal de N\u00edvel Superior","doi-asserted-by":"publisher","award":["Finance Code 001"],"award-info":[{"award-number":["Finance Code 001"]}],"id":[{"id":"10.13039\/501100002322","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100002322","name":"Coordena\u00e7\u00e3o de Aperfei\u00e7oamento de Pessoal de N\u00edvel Superior","doi-asserted-by":"publisher","award":["Finance Code 001"],"award-info":[{"award-number":["Finance Code 001"]}],"id":[{"id":"10.13039\/501100002322","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100002322","name":"Coordena\u00e7\u00e3o de Aperfei\u00e7oamento de Pessoal de N\u00edvel Superior","doi-asserted-by":"publisher","award":["Finance Code 001"],"award-info":[{"award-number":["Finance Code 001"]}],"id":[{"id":"10.13039\/501100002322","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100002322","name":"Coordena\u00e7\u00e3o de Aperfei\u00e7oamento de Pessoal de N\u00edvel Superior","doi-asserted-by":"publisher","award":["Finance Code 001"],"award-info":[{"award-number":["Finance Code 001"]}],"id":[{"id":"10.13039\/501100002322","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Sci Rep"],"abstract":"<jats:title>Abstract<\/jats:title>\n                  <jats:p>\n                    A fractional order output feedback controller for a lung ventilator is designed. This is based on a state-of-the-art electrical analogue model of the human respiratory system in the form of a network of resistors and fractional capacitors. The electrical input impedance of the adopted analogue can be suitably tuned to fit experimental ventilation impedance data. Furthermore, it can explicitly account for the different physiological fractal type characteristics associated with lung formation such as branching morphogenesis associated to the treelike tubular network and alveolar differentiation associated with the generation of specialized epithelial cells for gas exchange. A description of this electrical analogue in pseudo-state space is then proposed. The aim is to finally provide a control methodology within the scope of output feedback control, when the measured output which is the airflow through the trachea is directed to follow a specified reference. The control provides adequate air pressure input to generate this nominal airflow. The proposed control design includes a pseudo-state observer and a double leaky integrator. The gains involved are designed using constraints imposed through linear matrix inequalities (LMIs), which enforce a regional allocation of eigenvalues. The robustness of the control loop is analysed through an uncertainty matrix analysis linked directly to the model. It is observed that the proposed design can tolerate a relatively wide variation in physiological parameters (\n                    <jats:inline-formula>\n                      <jats:tex-math>$$\\pm 15\\%$$<\/jats:tex-math>\n                    <\/jats:inline-formula>\n                    ). The proposed formulation advances current control design approaches for mechanical ventilators and provides a generic methodology for the control of complex system with emergent responses as encountered in bioengineering.\n                  <\/jats:p>","DOI":"10.1038\/s41598-024-77654-6","type":"journal-article","created":{"date-parts":[[2025,10,7]],"date-time":"2025-10-07T08:13:07Z","timestamp":1759824787000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["Tracking control of air flow based on a fractional-order model of the lung impedance"],"prefix":"10.1038","volume":"15","author":[{"given":"Hadamez","family":"Kuzminskas","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Marcelo Carvalho Minhoto","family":"Teixeira","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Roberto Kawakami Harrop","family":"Galv\u00e3o","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Edvaldo","family":"Assun\u00e7\u00e3o","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Sillas","family":"Hadjiloucas","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","published-online":{"date-parts":[[2025,10,7]]},"reference":[{"key":"77654_CR1","doi-asserted-by":"publisher","first-page":"313","DOI":"10.1097\/00000542-195905000-00009","volume":"20","author":"MJ Frumin","year":"1959","unstructured":"Frumin, M. J., Bergman, N. A. & Holaday, D. A. Carbon dioxide and oxygen blood levels with a carbon dioxide controlled artificial respirator. J. Am. Soc. Anesthesiol. 20, 313\u2013320 (1959).","journal-title":"J. Am. Soc. Anesthesiol."},{"key":"77654_CR2","doi-asserted-by":"publisher","first-page":"846","DOI":"10.1007\/BF02478088","volume":"13","author":"Y Mitamura","year":"1975","unstructured":"Mitamura, Y., Mikami, T. & Yamamoto, K. A dual control system for assisting respiration. Med. Biol. Eng. 13, 846\u2013854 (1975).","journal-title":"Med. Biol. Eng."},{"key":"77654_CR3","doi-asserted-by":"crossref","unstructured":"Ritchie, R.\u00a0G., Ernst, E.\u00a0A., Pate, B.\u00a0L., Pearson, J. & Sheppard, L.\u00a0C. Closed-loop control of an anesthesia delivery system: Development and animal testing. IEEE Trans. Biomed. Eng. 437\u2013443 (1987).","DOI":"10.1109\/TBME.1987.326078"},{"key":"77654_CR4","doi-asserted-by":"publisher","first-page":"201","DOI":"10.1097\/00000542-197809000-00010","volume":"49","author":"RL Coon","year":"1978","unstructured":"Coon, R. L., Zuperku, E. J. & Kampine, J. P. Systemic arterial blood pH servocontrol of mechanical ventilation. Anesthesiology 49, 201\u2013204 (1978).","journal-title":"Anesthesiology"},{"key":"77654_CR5","doi-asserted-by":"publisher","first-page":"51","DOI":"10.1109\/10.277271","volume":"41","author":"TP Laubscher","year":"1994","unstructured":"Laubscher, T. P., Heinrichs, W., Weiler, N., Hartmann, G. & Brunner, J. X. An adaptive lung ventilation controller. IEEE Trans. Biomed. Eng. 41, 51\u201359 (1994).","journal-title":"IEEE Trans. Biomed. Eng."},{"key":"77654_CR6","first-page":"1402","volume":"110","author":"W Karzai","year":"2009","unstructured":"Karzai, W. & Schwarzkopf, K. Hypoxemia during one-lung ventilation: Prediction, prevention, and treatment. J. Am. Soc. Anesthesiologists 110, 1402\u20131411 (2009).","journal-title":"J. Am. Soc. Anesthesiologists"},{"key":"77654_CR7","doi-asserted-by":"publisher","first-page":"794","DOI":"10.1177\/0310057X0503300615","volume":"33","author":"J Pfitzner","year":"2005","unstructured":"Pfitzner, J. & Pfitzner, L. The theoretical basis for using apnoeic oxygenation via the non-ventilated lung during one-lung ventilation to delay the onset of arterial hypoxaemia. Anaesth. Intensive Care 33, 794\u2013800 (2005).","journal-title":"Anaesth. Intensive Care"},{"key":"77654_CR8","doi-asserted-by":"publisher","first-page":"766","DOI":"10.1111\/j.1399-6576.2008.01652.x","volume":"52","author":"G Cinnella","year":"2008","unstructured":"Cinnella, G. et al. Physiological effects of a lung-recruiting strategy applied during one-lung ventilation. Acta Anaesthesiol. Scand. 52, 766\u2013775 (2008).","journal-title":"Acta Anaesthesiol. Scand."},{"key":"77654_CR9","doi-asserted-by":"publisher","first-page":"500","DOI":"10.3389\/fped.2020.00500","volume":"8","author":"M Pavone","year":"2020","unstructured":"Pavone, M., Verrillo, E., Onofri, A., Caggiano, S. & Cutrera, R. Ventilators and ventilatory modalities. Front. Pediatr. 8, 500 (2020).","journal-title":"Front. Pediatr."},{"key":"77654_CR10","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1186\/s13054-021-03686-3","volume":"25","author":"P Pelosi","year":"2021","unstructured":"Pelosi, P. et al. Personalized mechanical ventilation in acute respiratory distress syndrome. Crit. Care 25, 1\u201310 (2021).","journal-title":"Crit. Care"},{"key":"77654_CR11","doi-asserted-by":"publisher","DOI":"10.1016\/j.semperi.2024.151886","volume":"48","author":"M Keszler","year":"2024","unstructured":"Keszler, M. & Abubakar, M. .\u00a0K. Volume-targeted ventilation. Semin. Perinatol. 48, 151886 (2024).","journal-title":"Semin. Perinatol."},{"key":"77654_CR12","doi-asserted-by":"publisher","first-page":"32","DOI":"10.1186\/s13054-022-03895-4","volume":"26","author":"F Mojoli","year":"2022","unstructured":"Mojoli, F. et al. Timing of inspiratory muscle activity detected from airway pressure and flow during pressure support ventilation: the waveform method. Crit. Care 26, 32 (2022).","journal-title":"Crit. Care"},{"key":"77654_CR13","doi-asserted-by":"crossref","unstructured":"Garmendia, O. et al. Low-cost, easy-to-build noninvasive pressure support ventilator for under-resourced regions: Open source hardware description, performance and feasibility testing. Eur. Respirat. J. 55 (2020).","DOI":"10.1183\/13993003.00846-2020"},{"key":"77654_CR14","doi-asserted-by":"publisher","first-page":"2301","DOI":"10.1007\/s00134-020-06206-z","volume":"46","author":"AH Jonkman","year":"2020","unstructured":"Jonkman, A. H. et al. Proportional modes of ventilation: Technology to assist physiology. Intensive Care Med. 46, 2301\u20132313 (2020).","journal-title":"Intensive Care Med."},{"key":"77654_CR15","doi-asserted-by":"publisher","first-page":"851","DOI":"10.1007\/s00134-021-06459-2","volume":"47","author":"DL Grieco","year":"2021","unstructured":"Grieco, D. L. et al. Non-invasive ventilatory support and high-flow nasal oxygen as first-line treatment of acute hypoxemic respiratory failure and ARDS. Intensive Care Med. 47, 851\u2013866 (2021).","journal-title":"Intensive Care Med."},{"key":"77654_CR16","doi-asserted-by":"publisher","first-page":"369","DOI":"10.1016\/j.arcontrol.2019.05.001","volume":"48","author":"SE Morton","year":"2019","unstructured":"Morton, S. E. et al. Optimising mechanical ventilation through model-based methods and automation. Annu. Rev. Control. 48, 369\u2013382 (2019).","journal-title":"Annu. Rev. Control."},{"key":"77654_CR17","doi-asserted-by":"publisher","first-page":"685","DOI":"10.1515\/mms-2017-0053","volume":"24","author":"J Glapi\u0144ski","year":"2017","unstructured":"Glapi\u0144ski, J. & Jab\u0142o\u0144ski, I. Minimization of ventilator-induced lung injury in ARDS patients - Part I: Complex model of mechanically ventilated ARDS lungs. Metrol. Meas. Syst. 24, 685\u2013699 (2017).","journal-title":"Metrol. Meas. Syst."},{"key":"77654_CR18","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1615\/CritRevBiomedEng.v32.10","volume":"32","author":"R Magin","year":"2004","unstructured":"Magin, R. Fractional calculus in bioengineering, part 1. Crit. Rev. Trade Biomed. Eng. 32, 1\u2013104 (2004).","journal-title":"Crit. Rev. Trade Biomed. Eng."},{"key":"77654_CR19","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-87553-3","volume-title":"Morphometry of the Human Lung","author":"ER Weibel","year":"1963","unstructured":"Weibel, E. R., Cournand, A. F. & Richards, D. W. Morphometry of the Human Lung Vol. 1 (Springer, Berlin, 1963)."},{"key":"77654_CR20","doi-asserted-by":"publisher","first-page":"1625","DOI":"10.1088\/0031-9155\/44\/7\/304","volume":"44","author":"V Sauret","year":"1999","unstructured":"Sauret, V., Goatman, K., Fleming, J. & Bailey, A. Semi-automated tabulation of the 3D topology and morphology of branching networks using CT: Application to the airway tree. Phys. Med. Biol. 44, 1625\u20131638 (1999).","journal-title":"Phys. Med. Biol."},{"key":"77654_CR21","doi-asserted-by":"publisher","first-page":"123","DOI":"10.1046\/j.0021-8782.2001.00018.x","volume":"200","author":"V Sauret","year":"2002","unstructured":"Sauret, V., Halson, P., Brown, I., Fleming, J. & Bailey, A. Study of the three-dimensional geometry of the central conducting airways in man using computed tomographic (CT) images. J. Anat. 200, 123\u2013134 (2002).","journal-title":"J. Anat."},{"key":"77654_CR22","doi-asserted-by":"publisher","first-page":"949","DOI":"10.1109\/TBME.2008.2007807","volume":"56","author":"CM Ionescu","year":"2008","unstructured":"Ionescu, C. M., Segers, P. & De Keyser, R. Mechanical properties of the respiratory system derived from morphologic insight. IEEE Trans. Biomed. Eng. 56, 949\u2013959 (2008).","journal-title":"IEEE Trans. Biomed. Eng."},{"key":"77654_CR23","doi-asserted-by":"publisher","first-page":"246","DOI":"10.1109\/TBME.2009.2030496","volume":"57","author":"CM Ionescu","year":"2009","unstructured":"Ionescu, C. M., Muntean, I., Tenreiro-Machado, J., De Keyser, R. & Abrudean, M. A theoretical study on modeling the respiratory tract with ladder networks by means of intrinsic fractal geometry. IEEE Trans. Biomed. Eng. 57, 246\u2013253 (2009).","journal-title":"IEEE Trans. Biomed. Eng."},{"key":"77654_CR24","first-page":"21","volume":"62","author":"C-M Ionescu","year":"2010","unstructured":"Ionescu, C.-M., Kosi\u0144ski, W. & De Keyser, R. Viscoelasticity and fractal structure in a model of human lungs. Arch. Mech. 62, 21\u201348 (2010).","journal-title":"Arch. Mech."},{"key":"77654_CR25","doi-asserted-by":"publisher","first-page":"83","DOI":"10.1109\/TBCAS.2010.2077636","volume":"5","author":"CM Ionescu","year":"2011","unstructured":"Ionescu, C. M., Tenreiro Machado, J. A. & De Keyser, R. Modelling of the lung impedance using a fractional-order ladder network with constant phase elements. IEEE Trans. Biomed. Circuits Syst. 5, 83\u201389 (2011).","journal-title":"IEEE Trans. Biomed. Circuits Syst."},{"key":"77654_CR26","doi-asserted-by":"publisher","first-page":"315","DOI":"10.1080\/03091900701862240","volume":"32","author":"C Ionescu","year":"2008","unstructured":"Ionescu, C. & De Keyser, R. Parametric models for characterizing respiratory input impedance. J. Med. Eng. Technol. 32, 315\u2013324 (2008).","journal-title":"J. Med. Eng. Technol."},{"key":"77654_CR27","doi-asserted-by":"publisher","first-page":"294","DOI":"10.1115\/1.3167615","volume":"51","author":"PJ Torvik","year":"1984","unstructured":"Torvik, P. J. & Bagley, R. L. On the appearance of the fractional derivative in the behavior of real materials. J. Appl. Mech. 51, 294\u2013298 (1984).","journal-title":"J. Appl. Mech."},{"key":"77654_CR28","doi-asserted-by":"publisher","first-page":"15","DOI":"10.1007\/s11043-005-3442-1","volume":"9","author":"K Adolfsson","year":"2005","unstructured":"Adolfsson, K., Enelund, M. & Olsson, P. On the fractional order model of viscoelasticity. Mech. Time-Depend. Mater. 9, 15\u201334 (2005).","journal-title":"Mech. Time-Depend. Mater."},{"key":"77654_CR29","doi-asserted-by":"publisher","first-page":"25","DOI":"10.1109\/81.817385","volume":"47","author":"A Oustaloup","year":"2000","unstructured":"Oustaloup, A., Levron, F., Mathieu, B. & Nanot, F. M. Frequency-band complex noninteger differentiator: Characterization and synthesis. IEEE Trans. Circuits Syst. I Fundam. Theory Appl. 47, 25\u201339 (2000).","journal-title":"IEEE Trans. Circuits Syst. I Fundam. Theory Appl."},{"key":"77654_CR30","doi-asserted-by":"publisher","first-page":"40","DOI":"10.1109\/MCAS.2010.938637","volume":"10","author":"AS Elwakil","year":"2010","unstructured":"Elwakil, A. S. Fractional-order circuits and systems: An emerging interdisciplinary research area. IEEE Circuits Syst. Mag. 10, 40\u201350 (2010).","journal-title":"IEEE Circuits Syst. Mag."},{"key":"77654_CR31","doi-asserted-by":"publisher","first-page":"465","DOI":"10.3233\/THC-2008-16607","volume":"16","author":"J Jossinet","year":"2008","unstructured":"Jossinet, J. Elementary electrodynamics. Technol. Health Care 16, 465\u2013474 (2008).","journal-title":"Technol. Health Care"},{"key":"77654_CR32","doi-asserted-by":"publisher","first-page":"61","DOI":"10.1016\/j.jare.2020.12.016","volume":"32","author":"M Ghita","year":"2021","unstructured":"Ghita, M., Copot, D. & Ionescu, C. M. Lung cancer dynamics using fractional order impedance modeling on a mimicked lung tumor setup. J. Adv. Res. 32, 61\u201371 (2021).","journal-title":"J. Adv. Res."},{"key":"77654_CR33","doi-asserted-by":"crossref","unstructured":"D\u2019Orsi, L., Borri, A. & De Gaetano, A. Mathematical modeling of lung mechanics and pressure-controlled ventilation design for barotrauma minimization: A numerical simulation study. Int. J. Robust Nonlinear Control (2024) (in press).","DOI":"10.1002\/rnc.7270"},{"key":"77654_CR34","doi-asserted-by":"publisher","first-page":"345","DOI":"10.1016\/j.isatra.2021.12.021","volume":"129","author":"DIR Almeida","year":"2022","unstructured":"Almeida, D. I. R. et al. Modeling and control of an invasive mechanical ventilation system using the active disturbances rejection control structure. ISA Trans. 129, 345\u2013354 (2022).","journal-title":"ISA Trans."},{"key":"77654_CR35","doi-asserted-by":"publisher","DOI":"10.1016\/j.conengprac.2021.104976","volume":"118","author":"D Garc\u00eda-Violini","year":"2022","unstructured":"Garc\u00eda-Violini, D., Faedo, N. & Cafiero, E. Modelling and pressure control of the expiratory cycle for mechanical ventilation systems. Control. Eng. Pract. 118, 104976 (2022).","journal-title":"Control. Eng. Pract."},{"key":"77654_CR36","doi-asserted-by":"publisher","first-page":"1819","DOI":"10.1109\/TCST.2023.3250966","volume":"31","author":"J Reinders","year":"2023","unstructured":"Reinders, J. et al. Repetitive control for Lur\u2019e-type systems: Application to mechanical ventilation. IEEE Trans. Control Syst. Technol. 31, 1819\u20131829 (2023).","journal-title":"IEEE Trans. Control Syst. Technol."},{"key":"77654_CR37","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-319-89981-7","volume-title":"Basics of Mechanical Ventilation","author":"H Poor","year":"2018","unstructured":"Poor, H. Basics of Mechanical Ventilation (Springer, 2018)."},{"key":"77654_CR38","doi-asserted-by":"crossref","unstructured":"Borrello, M. The application of controls in critical care ventilation. In Proceedings IEEE Conference on Control Technology and Applications 701\u2013718 (2021).","DOI":"10.1109\/CCTA48906.2021.9659125"},{"key":"77654_CR39","doi-asserted-by":"publisher","first-page":"3967","DOI":"10.1109\/TAC.2018.2884650","volume":"64","author":"E Weitenberg","year":"2018","unstructured":"Weitenberg, E. et al. Robust decentralized secondary frequency control in power systems: Merits and tradeoffs. IEEE Trans. Autom. Control 64, 3967\u20133982 (2018).","journal-title":"IEEE Trans. Autom. Control"},{"key":"77654_CR40","doi-asserted-by":"publisher","first-page":"1026","DOI":"10.1183\/09031936.03.00089403","volume":"22","author":"E Oostveen","year":"2003","unstructured":"Oostveen, E. et al. The forced oscillation technique in clinical practice: Methodology, recommendations and future developments. Eur. Respir. J. 22, 1026\u20131041 (2003).","journal-title":"Eur. Respir. J."},{"key":"77654_CR41","doi-asserted-by":"crossref","unstructured":"Lorenzo, C.\u00a0F. & Hartley, T.\u00a0T. Initialization in fractional order systems. In Proceedings 2001 European Control Conference (ECC) 1471\u20131476 (2001).","DOI":"10.23919\/ECC.2001.7076126"},{"key":"77654_CR42","doi-asserted-by":"publisher","first-page":"3117","DOI":"10.1016\/j.camwa.2012.03.099","volume":"64","author":"J-C Trigeassou","year":"2012","unstructured":"Trigeassou, J.-C., Maamri, N., Sabatier, J. & Oustaloup, A. State variables and transients of fractional order differential systems. Comput. Math. Appl. 64, 3117\u20133140 (2012).","journal-title":"Comput. Math. Appl."},{"key":"77654_CR43","doi-asserted-by":"publisher","first-page":"892","DOI":"10.1016\/j.camwa.2012.11.020","volume":"66","author":"J-C Trigeassou","year":"2013","unstructured":"Trigeassou, J.-C., Maamri, N. & Oustaloup, A. The infinite state approach: Origin and necessity. Comput. Math. Appl. 66, 892\u2013907 (2013).","journal-title":"Comput. Math. Appl."},{"key":"77654_CR44","doi-asserted-by":"crossref","unstructured":"Boyd, S., El Ghaoui, L., Feron, E. & Balakrishnan, V. Linear Matrix Inequalities in System and Control Theory (SIAM, 1994).","DOI":"10.1137\/1.9781611970777"},{"key":"77654_CR45","doi-asserted-by":"publisher","first-page":"358","DOI":"10.1109\/9.486637","volume":"41","author":"M Chilali","year":"1996","unstructured":"Chilali, M. & Gahinet, P. $$H_{\\infty }$$ design with pole placement constraints: An LMI approach. IEEE Trans. Autom. Control 41, 358\u2013367 (1996).","journal-title":"IEEE Trans. Autom. Control"},{"key":"77654_CR46","doi-asserted-by":"publisher","first-page":"2257","DOI":"10.1109\/9.811208","volume":"44","author":"M Chilali","year":"1999","unstructured":"Chilali, M., Gahinet, P. & Apkarian, P. Robust pole placement in LMI regions. IEEE Trans. Autom. Control 44, 2257\u20132270 (1999).","journal-title":"IEEE Trans. Autom. Control"},{"key":"77654_CR47","unstructured":"Zhang, X. & Chen, Y. D-stability based LMI criteria of stability and stabilization for fractional order systems. In Proceedings International Design Engineering Technical Conferences and Computers and Information in Engineering Conference vol. 57199, p. V009T07A029 (2015)."},{"key":"77654_CR48","doi-asserted-by":"crossref","unstructured":"Zhang, X. & Zhang, Y. D-admissibility criteria of singular fractional order systems. In Proceedings 2019 Chinese Control Conference (CCC) 1253\u20131257 (2019).","DOI":"10.23919\/ChiCC.2019.8865459"},{"key":"77654_CR49","unstructured":"Matignon, D. Stability results for fractional differential equations with applications to control processing. In Proceedings IMACS - IEEE SMC Computational Engineering in Systems Applications, Lille vol. 2, pp. 963\u2013968 (1996)."},{"key":"77654_CR50","doi-asserted-by":"publisher","first-page":"1594","DOI":"10.1016\/j.camwa.2009.08.003","volume":"59","author":"J Sabatier","year":"2010","unstructured":"Sabatier, J., Moze, M. & Farges, C. LMI stability conditions for fractional order systems. Comput. Math. Appl. 59, 1594\u20131609 (2010).","journal-title":"Comput. Math. Appl."},{"key":"77654_CR51","doi-asserted-by":"publisher","first-page":"152","DOI":"10.1109\/TAC.2009.2033738","volume":"55","author":"J-G Lu","year":"2010","unstructured":"Lu, J.-G. & Chen, Y.-Q. Robust stability and stabilization of fractional-order interval systems with the fractional order $$\\alpha$$: The $$0<\\alpha <1$$ case. IEEE Trans. Autom. Control 55, 152\u2013158 (2010).","journal-title":"IEEE Trans. Autom. Control"},{"key":"77654_CR52","doi-asserted-by":"publisher","first-page":"2423","DOI":"10.1109\/TNNLS.2016.2574842","volume":"28","author":"S Zhang","year":"2016","unstructured":"Zhang, S., Yu, Y. & Yu, J. LMI conditions for global stability of fractional-order neural networks. IEEE Trans. Neural Netw. Learn. Syst. 28, 2423\u20132433 (2016).","journal-title":"IEEE Trans. Neural Netw. Learn. Syst."},{"key":"77654_CR53","volume-title":"Modern Control Engineering. Prentice-Hall Electrical Engineering Series. Instrumentation and controls series","author":"K Ogata","year":"2010","unstructured":"Ogata, K. Modern Control Engineering. Prentice-Hall Electrical Engineering Series. Instrumentation and Controls Series illustrat edn. (Prentice Hall, 2010).","edition":"illustrat"},{"key":"77654_CR54","volume-title":"Modern Control Systems","author":"RC Dorf","year":"2017","unstructured":"Dorf, R. C. & Bishop, R. H. Modern Control Systems 13th global edition. (Pearson Education, 2017).","edition":"13th global edi"},{"key":"77654_CR55","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-662-09775-5","volume-title":"Robust Control Systems: Theory and Case Studies","author":"U Mackenroth","year":"2004","unstructured":"Mackenroth, U. Robust Control Systems: Theory and Case Studies (Springer, 2004)."},{"key":"77654_CR56","doi-asserted-by":"crossref","unstructured":"Matignon, D. & d\u2019Andrea Novel, B. Observer-based controllers for fractional differential systems. In Proceedings 36th IEEE Conference on Decision and Control vol.\u00a05, pp. 4967\u20134972 (1997).","DOI":"10.1109\/CDC.1997.649835"},{"key":"77654_CR57","doi-asserted-by":"publisher","first-page":"229","DOI":"10.1049\/iet-cta.2010.0484","volume":"6","author":"Y-H Lan","year":"2012","unstructured":"Lan, Y.-H., Huang, H.-X. & Zhou, Y. Observer-based robust control of a $$(1\\le a<2)$$ fractional-order uncertain systems: A linear matrix inequality approach. IET Control Theory Appl. 6, 229\u2013234 (2012).","journal-title":"IET Control Theory Appl."},{"key":"77654_CR58","doi-asserted-by":"publisher","first-page":"8217126","DOI":"10.1155\/2017\/8217126","volume":"2017","author":"J Qiu","year":"2017","unstructured":"Qiu, J. & Ji, Y. Observer-based robust controller design for nonlinear fractional-order uncertain systems via LMI. Math. Probl. Eng. 2017, 8217126 (2017).","journal-title":"Math. Probl. Eng."},{"key":"77654_CR59","doi-asserted-by":"crossref","unstructured":"Charef, A. Analogue realisation of fractional-order integrator, differentiator and fractional PI$$^\\lambda$$D$$^\\mu$$ controller. In IEE Proceedings - Control Theory and Applications, vol. 153, 714\u2013720 (2006).","DOI":"10.1049\/ip-cta:20050019"},{"key":"77654_CR60","doi-asserted-by":"publisher","first-page":"1484","DOI":"10.1109\/TCSI.2018.2885013","volume":"66","author":"MF Tolba","year":"2019","unstructured":"Tolba, M. F., Said, L. A., Madian, A. H. & Radwan, A. G. FPGA implementation of the fractional order integrator\/differentiator: Two approaches and applications. IEEE Trans. Circuits Syst. I Regul. Pap. 66, 1484\u20131495 (2019).","journal-title":"IEEE Trans. Circuits Syst. I Regul. Pap."},{"key":"77654_CR61","unstructured":"Tepljakov, A. FOMCON toolbox for MATLAB https:\/\/github.com\/extall\/fomcon-matlab\/releases\/tag\/v1.50.4, github (2024)."},{"key":"77654_CR62","doi-asserted-by":"crossref","unstructured":"Tepljakov, A. FOMCON: Fractional-order modeling and control toolbox. In Fractional-order Modeling and Control of Dynamic Systems 107\u2013129 (2017).","DOI":"10.1007\/978-3-319-52950-9_6"},{"key":"77654_CR63","doi-asserted-by":"crossref","unstructured":"L\u00f6fberg, J. YALMIP: A toolbox for modeling and optimization in MATLAB. In Proceedings 2004 IEEE International Conference on Robotics and Automation 284\u2013289 (2004).","DOI":"10.1109\/CACSD.2004.1393890"},{"key":"77654_CR64","doi-asserted-by":"publisher","first-page":"625","DOI":"10.1080\/10556789908805766","volume":"11","author":"JF Sturm","year":"1999","unstructured":"Sturm, J. F. Using SeDuMi $$1.02$$, a MATLAB toolbox for optimization over symmetric cones. Optim. Methods Softw. 11, 625\u2013653 (1999).","journal-title":"Optim. Methods Softw."},{"key":"77654_CR65","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-030-55408-8","volume-title":"Artificial Ventilation: A Basic Clinical Guide","author":"DJ Baker","year":"2020","unstructured":"Baker, D. J. Artificial Ventilation: A Basic Clinical Guide 2nd edn. (Springer, 2020).","edition":"2nd"},{"key":"77654_CR66","doi-asserted-by":"publisher","first-page":"9281","DOI":"10.1038\/s41598-023-36506-5","volume":"13","author":"D Acharya","year":"2023","unstructured":"Acharya, D. & Das, D. K. A novel PID controller for pressure control of artificial ventilator using optimal rule based fuzzy inference system with RCTO algorithm. Sci. Rep. 13, 9281 (2023).","journal-title":"Sci. Rep."},{"key":"77654_CR67","doi-asserted-by":"publisher","first-page":"21275","DOI":"10.1038\/s41598-023-41881-0","volume":"13","author":"J Casta\u00f1o","year":"2023","unstructured":"Casta\u00f1o, J. et al. Electropneumatic system for the simulation of the pulmonary viscoelastic effect in a mechanical ventilation scenario. Sci. Rep. 13, 21275 (2023).","journal-title":"Sci. Rep."},{"key":"77654_CR68","first-page":"20200990","volume":"477","author":"J Guo","year":"2021","unstructured":"Guo, J., Yin, Y. & Peng, G. Fractional-order viscoelastic model of musculoskeletal tissues: Correlation with fractals. Proc. R. Soc. A. Math. Phys. Eng. Sci. 477, 20200990 (2021).","journal-title":"Proc. R. Soc. A. Math. Phys. Eng. Sci."},{"key":"77654_CR69","volume-title":"General Fractional Derivatives with Applications in Viscoelasticity","author":"X-J Yang","year":"2020","unstructured":"Yang, X.-J., Gao, F. & Ju, Y. General Fractional Derivatives with Applications in Viscoelasticity (Academic Press, 2020)."},{"key":"77654_CR70","doi-asserted-by":"crossref","unstructured":"Shitikova, M. Fractional operator viscoelastic models in dynamic problems of mechanics of solids: A review. Mech. Solids 1\u201333 (2022).","DOI":"10.3103\/S0025654422010022"},{"key":"77654_CR71","doi-asserted-by":"publisher","first-page":"1962","DOI":"10.1007\/s00330-002-1379-1","volume":"12","author":"H-U Kauczor","year":"2002","unstructured":"Kauczor, H.-U., Hanke, A. & van Beek, E. J. Assessment of lung ventilation by MR imaging: Current status and future perspectives. Eur. Radiol. 12, 1962\u20131970 (2002).","journal-title":"Eur. Radiol."},{"key":"77654_CR72","doi-asserted-by":"publisher","first-page":"312","DOI":"10.1002\/mrm.28114","volume":"84","author":"MM Willmering","year":"2020","unstructured":"Willmering, M. M. et al. Improved pulmonary $$^{129}$$Xe ventilation imaging via 3D-spiral UTE MRI. Magn. Reson. Med. 84, 312\u2013320 (2020).","journal-title":"Magn. Reson. Med."},{"key":"77654_CR73","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1186\/s13613-020-00725-0","volume":"10","author":"DE Hurtado","year":"2020","unstructured":"Hurtado, D. E. et al. Progression of regional lung strain and heterogeneity in lung injury: Assessing the evolution under spontaneous breathing and mechanical ventilation. Ann. Intensive Care 10, 1\u201310 (2020).","journal-title":"Ann. Intensive Care"},{"key":"77654_CR74","doi-asserted-by":"crossref","unstructured":"Galv\u00e3o, R. K.\u00a0H. & Hadjiloucas, S. Measurement and control of emergent phenomena emulated by resistive-capacitive networks, using fractional-order internal model control and external adaptive control. Rev. Sci. Instrum. 90 (2019).","DOI":"10.1063\/1.5097743"},{"key":"77654_CR75","first-page":"896","volume":"62","author":"LA Jacyntho","year":"2015","unstructured":"Jacyntho, L. A. et al. Identification of fractional-order transfer functions using a step excitation. IEEE Trans. Circuits Syst. II Express Briefs 62, 896\u2013900 (2015).","journal-title":"IEEE Trans. Circuits Syst. II Express Briefs"},{"key":"77654_CR76","doi-asserted-by":"publisher","first-page":"6002","DOI":"10.1039\/D0SM00354A","volume":"16","author":"A Bonfanti","year":"2020","unstructured":"Bonfanti, A., Kaplan, J. L., Charras, G. & Kabla, A. Fractional viscoelastic models for power-law materials. Soft Matter 16, 6002\u20136020 (2020).","journal-title":"Soft Matter"},{"key":"77654_CR77","first-page":"1","volume":"72","author":"Q Deng","year":"2023","unstructured":"Deng, Q., Qiu, D., Xie, Z., Zhang, B. & Chen, Y. Online SOC estimation of supercapacitor energy storage system based on fractional-order model. IEEE Trans. Instrum. Meas. 72, 1\u201310 (2023).","journal-title":"IEEE Trans. Instrum. Meas."}],"container-title":["Scientific Reports"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.nature.com\/articles\/s41598-024-77654-6.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.nature.com\/articles\/s41598-024-77654-6","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.nature.com\/articles\/s41598-024-77654-6.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,7]],"date-time":"2025-10-07T21:05:21Z","timestamp":1759871121000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.nature.com\/articles\/s41598-024-77654-6"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,10,7]]},"references-count":77,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2025,12]]}},"alternative-id":["77654"],"URL":"https:\/\/doi.org\/10.1038\/s41598-024-77654-6","relation":{"has-preprint":[{"id-type":"doi","id":"10.21203\/rs.3.rs-3881657\/v1","asserted-by":"object"}]},"ISSN":["2045-2322"],"issn-type":[{"value":"2045-2322","type":"electronic"}],"subject":[],"published":{"date-parts":[[2025,10,7]]},"assertion":[{"value":"20 January 2024","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"24 October 2024","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"7 October 2025","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"The authors declare no competing interests.","order":1,"name":"Ethics","group":{"name":"EthicsHeading","label":"Competing interests"}}],"article-number":"34832"}}