{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,17]],"date-time":"2026-06-17T17:15:33Z","timestamp":1781716533948,"version":"3.54.5"},"reference-count":36,"publisher":"MDPI AG","issue":"12","license":[{"start":{"date-parts":[[2024,12,8]],"date-time":"2024-12-08T00:00:00Z","timestamp":1733616000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Fondo Nacional de Desarrollo Cient\u0131fico y Tecnologico","award":["3200854"],"award-info":[{"award-number":["3200854"]}]},{"name":"Fondo Nacional de Desarrollo Cient\u0131fico y Tecnologico","award":["3200853"],"award-info":[{"award-number":["3200853"]}]},{"name":"Fondo Nacional de Desarrollo Cient\u0131fico y Tecnologico","award":["062113AB"],"award-info":[{"award-number":["062113AB"]}]},{"name":"Fondo Nacional de Desarrollo Cient\u0131fico y Tecnologico","award":["PID2020-112871RB-C21\/AEI"],"award-info":[{"award-number":["PID2020-112871RB-C21\/AEI"]}]},{"name":"Fondo Nacional de Desarrollo Cient\u0131fico y Tecnologico","award":["062413EAB"],"award-info":[{"award-number":["062413EAB"]}]},{"name":"Univ. de Santiago de Chile, Direcci\u00f3n de Investigaci\u00f3n Cient\u00edfica y Tecnol\u00f3gica (DICYT)","award":["3200854"],"award-info":[{"award-number":["3200854"]}]},{"name":"Univ. de Santiago de Chile, Direcci\u00f3n de Investigaci\u00f3n Cient\u00edfica y Tecnol\u00f3gica (DICYT)","award":["3200853"],"award-info":[{"award-number":["3200853"]}]},{"name":"Univ. de Santiago de Chile, Direcci\u00f3n de Investigaci\u00f3n Cient\u00edfica y Tecnol\u00f3gica (DICYT)","award":["062113AB"],"award-info":[{"award-number":["062113AB"]}]},{"name":"Univ. de Santiago de Chile, Direcci\u00f3n de Investigaci\u00f3n Cient\u00edfica y Tecnol\u00f3gica (DICYT)","award":["PID2020-112871RB-C21\/AEI"],"award-info":[{"award-number":["PID2020-112871RB-C21\/AEI"]}]},{"name":"Univ. de Santiago de Chile, Direcci\u00f3n de Investigaci\u00f3n Cient\u00edfica y Tecnol\u00f3gica (DICYT)","award":["062413EAB"],"award-info":[{"award-number":["062413EAB"]}]},{"name":"Agencia Estatal de Investigaci\u00f3n","award":["3200854"],"award-info":[{"award-number":["3200854"]}]},{"name":"Agencia Estatal de Investigaci\u00f3n","award":["3200853"],"award-info":[{"award-number":["3200853"]}]},{"name":"Agencia Estatal de Investigaci\u00f3n","award":["062113AB"],"award-info":[{"award-number":["062113AB"]}]},{"name":"Agencia Estatal de Investigaci\u00f3n","award":["PID2020-112871RB-C21\/AEI"],"award-info":[{"award-number":["PID2020-112871RB-C21\/AEI"]}]},{"name":"Agencia Estatal de Investigaci\u00f3n","award":["062413EAB"],"award-info":[{"award-number":["062413EAB"]}]},{"name":"Vicerrector\u00eda de Investigaci\u00f3n, Innovaci\u00f3n y Creaci\u00f3n, USACH, Proyecto DICYT","award":["3200854"],"award-info":[{"award-number":["3200854"]}]},{"name":"Vicerrector\u00eda de Investigaci\u00f3n, Innovaci\u00f3n y Creaci\u00f3n, USACH, Proyecto DICYT","award":["3200853"],"award-info":[{"award-number":["3200853"]}]},{"name":"Vicerrector\u00eda de Investigaci\u00f3n, Innovaci\u00f3n y Creaci\u00f3n, USACH, Proyecto DICYT","award":["062113AB"],"award-info":[{"award-number":["062113AB"]}]},{"name":"Vicerrector\u00eda de Investigaci\u00f3n, Innovaci\u00f3n y Creaci\u00f3n, USACH, Proyecto DICYT","award":["PID2020-112871RB-C21\/AEI"],"award-info":[{"award-number":["PID2020-112871RB-C21\/AEI"]}]},{"name":"Vicerrector\u00eda de Investigaci\u00f3n, Innovaci\u00f3n y Creaci\u00f3n, USACH, Proyecto DICYT","award":["062413EAB"],"award-info":[{"award-number":["062413EAB"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>The ongoing development of gain-scheduled filters is motivated by the estimation of the sideslip angle of ground vehicles. The present work proposes an approach based on finite-frequency specifications and an energy-to-peak (E2P) index for designing linear parameter-varying (LPV) filters. After reporting a new theoretical result, analysis and synthesis conditions are proposed for gain-scheduled and robust filters. Their properties are tested and illustrated using a simulated ground vehicle system via a comparative study, highlighting the advantages of the proposed approach.<\/jats:p>","DOI":"10.3390\/sym16121627","type":"journal-article","created":{"date-parts":[[2024,12,9]],"date-time":"2024-12-09T06:16:14Z","timestamp":1733724974000},"page":"1627","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["Gain-Scheduled Energy-to-Peak Approach for Vehicle Sideslip Angle Filtering"],"prefix":"10.3390","volume":"16","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-4796-2744","authenticated-orcid":false,"given":"Taha","family":"Zoulagh","sequence":"first","affiliation":[{"name":"Identification and Control Laboratory, Department of Electrical Engineering, University of Santiago of Chile, Santiago 9170124, Chile"},{"name":"GIPSA-Lab, D\u00e9partment de Physique, Universit\u00e9 Grenoble Alpes, 38000 Grenoble, France"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-1098-275X","authenticated-orcid":false,"given":"Hicham","family":"El Aiss","sequence":"additional","affiliation":[{"name":"Identification and Control Laboratory, Department of Electrical Engineering, University of Santiago of Chile, Santiago 9170124, Chile"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-4046-3136","authenticated-orcid":false,"given":"Fernando","family":"Tadeo","sequence":"additional","affiliation":[{"name":"Institute of Sustainable Processes, Universidad de Valladolid, 47002 Valladolid, Spain"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-4776-0894","authenticated-orcid":false,"given":"Badreddine","family":"El Haiek","sequence":"additional","affiliation":[{"name":"Identification and Control Laboratory, Department of Electrical Engineering, University of Santiago of Chile, Santiago 9170124, Chile"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-7183-2662","authenticated-orcid":false,"given":"Karina A.","family":"Barbosa","sequence":"additional","affiliation":[{"name":"Identification and Control Laboratory, Department of Electrical Engineering, University of Santiago of Chile, Santiago 9170124, Chile"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Abdelaziz","family":"Hmamed","sequence":"additional","affiliation":[{"name":"Faculty of Engineering, Private University Campus of Fez, Fez 30040, Morocco"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2024,12,8]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"124","DOI":"10.1109\/TCST.2019.2949539","article-title":"Yaw rate and sideslip angle control through single input single output direct yaw moment control","volume":"29","author":"Lenzo","year":"2020","journal-title":"IEEE Trans. Control. Syst. Technol."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"799","DOI":"10.1016\/j.mechatronics.2009.04.005","article-title":"Yaw stability control of a steer-by-wire equipped vehicle via active front wheel steering","volume":"19","author":"Zheng","year":"2009","journal-title":"Mechatronics"},{"key":"ref_3","doi-asserted-by":"crossref","unstructured":"Zhang, H., Wang, R., and Wang, J. (2023). Sideslip angle estimation of an electric ground vehicle via finite-frequency H\u221e approach. Robust Gain-Scheduled Estimation and Control of Electrified Vehicles via LPV Technique, Springer.","DOI":"10.1007\/978-981-19-8509-6"},{"key":"ref_4","doi-asserted-by":"crossref","unstructured":"Liu, C., and Yao, J. (2022, January 9\u201311). Sideslip Angle Estimation for Lateral Vehicle Control with Delayed Output Measurements. Proceedings of the 2022 International Conference on Advanced Robotics and Mechatronics (ICARM), Guilin, China.","DOI":"10.1109\/ICARM54641.2022.9959337"},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"200","DOI":"10.1109\/TTE.2015.2511659","article-title":"Sideslip Angle Estimation of an Electric Ground Vehicle via Finite-Frequency H\u221e Approach","volume":"2","author":"Zhang","year":"2015","journal-title":"IEEE Trans. Transp. Electrif."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"10435","DOI":"10.1109\/TVT.2020.3008222","article-title":"Robust H\u221e Filtering for Vehicle Sideslip Angle With Quantization and Data Dropouts","volume":"69","author":"Chang","year":"2020","journal-title":"IEEE Trans. Veh. Technol."},{"key":"ref_7","doi-asserted-by":"crossref","unstructured":"Hellani, D.E., Hajjaji, A.E., Ceschi, R., and Aitouche, A. (2018, January 19\u201322). Sideslip Angle Estimation of Ground Vehicles in a Finite Frequency Domain Through H\u221e Approach. Proceedings of the 2018 26th Mediterranean Conference on Control and Automation (MED), Zadar, Croatia.","DOI":"10.1109\/MED.2018.8442765"},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"191","DOI":"10.1016\/j.sigpro.2017.08.022","article-title":"Finite frequency H\u221e filter design for TS fuzzy systems: New approach","volume":"143","author":"Ceschi","year":"2018","journal-title":"Signal Process."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"41","DOI":"10.1109\/TAC.2004.840475","article-title":"Generalized KYP Lemma: Unified frequency domain inequalities with design applications","volume":"50","author":"Iwasaki","year":"2005","journal-title":"IEEE Trans. Autom. Control"},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"161","DOI":"10.1016\/j.ifacol.2018.11.145","article-title":"L2-gain filter design for continuous-time LPV systems in finite frequency domain","volume":"51","author":"Frezzatto","year":"2018","journal-title":"IFAC-PapersOnLine"},{"key":"ref_11","unstructured":"Gao, H., and Li, X. (2016). Robust Filtering for Uncertain Systems, Springer."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"2667","DOI":"10.1016\/j.sigpro.2010.03.011","article-title":"Improved robust energy-to-peak filtering for uncertain linear systems","volume":"90","author":"Zhang","year":"2010","journal-title":"Signal Process."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"94","DOI":"10.1109\/9.8655","article-title":"Convolution and Hankel operator norms for linear systems","volume":"34","author":"Wilson","year":"1989","journal-title":"IEEE Trans. Autom. Control"},{"key":"ref_14","first-page":"126729","article-title":"Robust energy-to-peak filter design for a class of unstable polytopic systems with a macroeconomic application","volume":"420","author":"Gyurkovics","year":"2021","journal-title":"Appl. Math. Comput."},{"key":"ref_15","doi-asserted-by":"crossref","unstructured":"Zhang, H., and Wang, J. (2018). Robust gain-scheduling control of vehicle lateral dynamics through AFS\/DYC. Modeling, Dynamics and Control of Electrified Vehicles, Elsevier.","DOI":"10.1016\/B978-0-12-812786-5.00010-0"},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"2343","DOI":"10.1007\/s41939-023-00329-8","article-title":"Robust H\u221e filtering and time-varying delay compensation for car suspension systems: A comprehensive approach to reduced disturbance and enhanced estimation","volume":"7","author":"Liao","year":"2024","journal-title":"Multiscale Multidiscip. Model. Exp. Des."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"338","DOI":"10.1016\/j.mechatronics.2014.08.003","article-title":"Robust energy-to-peak sideslip angle estimation with applications to ground vehicles","volume":"30","author":"Zhang","year":"2015","journal-title":"Mechatronics"},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"968","DOI":"10.1080\/00423114.2022.2062011","article-title":"Gain-scheduling LPV synthesis H\u221e robust lateral motion control for path following of autonomous vehicle via coordination of steering and braking","volume":"61","author":"Cao","year":"2023","journal-title":"Veh. Syst. Dyn."},{"key":"ref_19","doi-asserted-by":"crossref","unstructured":"Aslam, M.S., Bilal, H., and Anjum, Z. (2024). Gain-scheduled filter design with different time delays for TS fuzzy systems. Trans. Inst. Meas. Control, 01423312241274009.","DOI":"10.1177\/01423312241274009"},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"1884","DOI":"10.1109\/TSMC.2016.2563390","article-title":"Finite Frequency L2 \u2212 L\u221e Filtering of TS Fuzzy Systems With Unknown Membership Functions","volume":"47","author":"Li","year":"2016","journal-title":"IEEE Trans. Syst. Man Cybern. Syst."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"1024","DOI":"10.1109\/LCSYS.2024.3406492","article-title":"A New Approach to the Energy-to-Peak Performance Analysis of Continuous-Time Markov Jump Linear Systems","volume":"8","author":"Todorov","year":"2024","journal-title":"IEEE Control Syst. Lett."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"2421","DOI":"10.1080\/00207721.2022.2053232","article-title":"Resilient energy-to-peak filtering for linear parameter-varying systems under random access protocol","volume":"53","author":"Yu","year":"2022","journal-title":"Int. J. Syst. Sci."},{"key":"ref_23","doi-asserted-by":"crossref","unstructured":"van Waarde, H.J., and Camlibel, M.K. (2021, January 13\u201317). A matrix Finsler\u2019s lemma with applications to data-driven control. Proceedings of the 2021 60th IEEE Conference on Decision and Control (CDC), Austin, TX, USA.","DOI":"10.1109\/CDC45484.2021.9683285"},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"3110","DOI":"10.1109\/TSMC.2024.3354940","article-title":"Design of protocol-based finite-time memory fault detection scheme with circuit system application","volume":"54","author":"Hu","year":"2024","journal-title":"IEEE Trans. Syst. Man Cybern. Syst."},{"key":"ref_25","first-page":"344","article-title":"Vehicle dynamics and motion simulation versus experiment","volume":"107","author":"Lozia","year":"1998","journal-title":"SAE Trans."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"186","DOI":"10.1080\/00423114.2013.868500","article-title":"Validation of vehicle dynamics simulation models\u2014A review","volume":"52","author":"Kutluay","year":"2014","journal-title":"Veh. Syst. Dyn."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"331","DOI":"10.1007\/s12239-010-0041-1","article-title":"Effect of vehicle model on the estimation of lateral vehicle dynamics","volume":"11","author":"Kim","year":"2010","journal-title":"Int. J. Automot. Technol."},{"key":"ref_28","doi-asserted-by":"crossref","unstructured":"Das, S. (2021, January 26\u201327). Vehicle Dynamics Modelling: Lateral and Longitudinal. Proceedings of the 2021 8th International Conference on Signal Processing and Integrated Networks (SPIN), Noida, India.","DOI":"10.1109\/SPIN52536.2021.9566093"},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"81","DOI":"10.1016\/j.sysconle.2004.11.016","article-title":"Robust stability of time varying polytopic systems","volume":"55","author":"Geromel","year":"2006","journal-title":"Syst. Contro. Lett."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"681","DOI":"10.1016\/j.sysconle.2004.11.007","article-title":"Time domain interpretations of frequency domain inequalities on (semi) finite ranges","volume":"54","author":"Iwasaki","year":"2005","journal-title":"Syst. Control Lett."},{"key":"ref_31","doi-asserted-by":"crossref","unstructured":"de Oliveira, M.C., and Skelton, R.E. (2001). Stability tests for constrained linear systems. Perspectives in Robust Control, Springer.","DOI":"10.1007\/BFb0110624"},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"356","DOI":"10.1109\/9.50357","article-title":"Robust stabilization of uncertain linear systems: Quadratic stabilizability and H\u221e control theory","volume":"35","author":"Khargonekar","year":"1990","journal-title":"IEEE Trans. Autom. Control"},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"378","DOI":"10.1002\/acs.2848","article-title":"Homogenous polynomial H\u221e filtering for uncertain discrete-time systems: A descriptor approach","volume":"32","author":"Zoulagh","year":"2018","journal-title":"Int. J. Adapt. Control Signal Process."},{"key":"ref_34","first-page":"941","article-title":"Polynomial static output feedback H\u221e control for continuous-time linear systems via descriptor approach","volume":"13","author":"Zoulagh","year":"2017","journal-title":"Int. J. Innov. Comput. Inf. Control"},{"key":"ref_35","unstructured":"Lofberg, J. (May, January 26). YALMIP: A toolbox for modeling and optimization in MATLAB. Proceedings of the 2004 IEEE international conference on robotics and automation (IEEE Cat. No. 04CH37508), New Orleans, LA, USA."},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"625","DOI":"10.1080\/10556789908805766","article-title":"Using SeDuMi 1.02, a MATLAB toolbox for optimization over symmetric cones","volume":"11","author":"Sturm","year":"1999","journal-title":"Optim. Methods Softw."}],"container-title":["Symmetry"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2073-8994\/16\/12\/1627\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T16:49:52Z","timestamp":1760114992000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2073-8994\/16\/12\/1627"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,12,8]]},"references-count":36,"journal-issue":{"issue":"12","published-online":{"date-parts":[[2024,12]]}},"alternative-id":["sym16121627"],"URL":"https:\/\/doi.org\/10.3390\/sym16121627","relation":{},"ISSN":["2073-8994"],"issn-type":[{"value":"2073-8994","type":"electronic"}],"subject":[],"published":{"date-parts":[[2024,12,8]]}}}