{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,11,21]],"date-time":"2025-11-21T18:04:41Z","timestamp":1763748281278,"version":"3.37.3"},"reference-count":38,"publisher":"Springer Science and Business Media LLC","issue":"4","license":[{"start":{"date-parts":[[2020,10,15]],"date-time":"2020-10-15T00:00:00Z","timestamp":1602720000000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"},{"start":{"date-parts":[[2020,10,15]],"date-time":"2020-10-15T00:00:00Z","timestamp":1602720000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Comp. Appl. Math."],"published-print":{"date-parts":[[2020,12]]},"DOI":"10.1007\/s40314-020-01354-w","type":"journal-article","created":{"date-parts":[[2020,10,15]],"date-time":"2020-10-15T22:02:20Z","timestamp":1602799340000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":4,"title":["Distributed functional observers for fractional-order time-varying interconnected time-delay systems"],"prefix":"10.1007","volume":"39","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-2028-3784","authenticated-orcid":false,"given":"Dinh Cong","family":"Huong","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2020,10,15]]},"reference":[{"key":"1354_CR1","doi-asserted-by":"publisher","DOI":"10.1002\/mma.6701","author":"ZS Aghayan","year":"2020","unstructured":"Aghayan ZS, Alfi A (2020) Stability analysis of fractional order neutral-type systems considering time varying delays, nonlinear perturbations, and input saturation. Math Methods Appl Sci. https:\/\/doi.org\/10.1002\/mma.6701","journal-title":"Math Methods Appl Sci"},{"key":"1354_CR2","doi-asserted-by":"publisher","first-page":"542","DOI":"10.1016\/j.jmaa.2006.01.087","volume":"325","author":"E Ahmed","year":"2007","unstructured":"Ahmed E, El-Sayed AMA, El-Saka HAA (2007) Equilibrium points, stability and numerical solutions of fractional-order predator-prey and rabies models. J Math Anal Appl 325:542\u2013553","journal-title":"J Math Anal Appl"},{"key":"1354_CR3","doi-asserted-by":"publisher","first-page":"304","DOI":"10.2514\/3.20641","volume":"14","author":"RL Bagley","year":"1991","unstructured":"Bagley RL, Calico RA (1991) Fractional order state equations for the control of viscoelastically damped structures. J Guidance Control Dyn 14:304\u2013311","journal-title":"J Guidance Control Dyn"},{"key":"1354_CR4","doi-asserted-by":"publisher","first-page":"491","DOI":"10.1109\/9.911430","volume":"46","author":"M Darouach","year":"2001","unstructured":"Darouach M (2001) Linear functional observers for systems with delays in state variables. IEEE Trans Autom Control 46:491\u2013496","journal-title":"IEEE Trans Autom Control"},{"key":"1354_CR5","doi-asserted-by":"publisher","first-page":"386","DOI":"10.1016\/j.mcm.2009.04.019","volume":"50","author":"Y Ding","year":"2009","unstructured":"Ding Y, Ye H (2009) A fractional-order differential equation model of HIV infection of CD4$$^+$$ T-cells. Math Comput Modell 50:386\u2013392","journal-title":"Math Comput Modell"},{"key":"1354_CR6","volume-title":"Generalized sylvester equations: unified parametric solutions","author":"GR Duan","year":"2014","unstructured":"Duan GR (2014) Generalized sylvester equations: unified parametric solutions. CRC Press, Boca Raton"},{"key":"1354_CR7","doi-asserted-by":"publisher","first-page":"650","DOI":"10.1016\/j.cnsns.2014.10.008","volume":"22","author":"MA Duarte-Mermoud","year":"2015","unstructured":"Duarte-Mermoud MA, Aguila-Camacho N, Gallegos JA, Castro-Linares R (2015) Using general quadratic Lyapunov functions to prove Lyapunov uniform stability for fractional order systems. Commun Nonlinear Sci Numer Simul 22:650\u2013659","journal-title":"Commun Nonlinear Sci Numer Simul"},{"key":"1354_CR8","doi-asserted-by":"crossref","first-page":"161","DOI":"10.1016\/j.amc.2016.04.039","volume":"287\u2013288","author":"JA Gallegos","year":"2016","unstructured":"Gallegos JA, Duarte MA (2016) On the Lyapunov theory for fractional order systems. Appl Math Comput 287\u2013288:161\u2013170","journal-title":"Appl Math Comput"},{"key":"1354_CR9","doi-asserted-by":"publisher","first-page":"647","DOI":"10.1007\/s12555-018-0155-1","volume":"17","author":"DK Gu","year":"2019","unstructured":"Gu DK, Liu LW, Duan GR (2019) A parametric method of linear functional observers for linear time-varying systems. Int J Control Autom Syst 17:647\u2013656","journal-title":"Int J Control Autom Syst"},{"key":"1354_CR10","doi-asserted-by":"publisher","first-page":"19398","DOI":"10.1109\/ACCESS.2020.2967813","volume":"8","author":"DK Gu","year":"2020","unstructured":"Gu DK, Liu QZ, Yang J (2020) Linear function observers for linear time-varying systems with time-delay: a parametric approach. IEEE Access 8:19398\u201319405","journal-title":"IEEE Access"},{"key":"1354_CR11","doi-asserted-by":"publisher","first-page":"2405","DOI":"10.1049\/iet-cta.2015.0108","volume":"9","author":"DC Huong","year":"2015","unstructured":"Huong DC, Trinh H (2015) Method for computing state transformations of time-delay systems. IET Control Theory Appl 9:2405\u20132413","journal-title":"IET Control Theory Appl"},{"key":"1354_CR12","doi-asserted-by":"publisher","first-page":"3487","DOI":"10.1016\/j.jfranklin.2016.06.033","volume":"353","author":"DC Huong","year":"2016","unstructured":"Huong DC, Trinh H (2016) New state transformations of time-delay systems with multiple delays and their applications to state observer design. J Franklin Inst 353:3487\u20133523","journal-title":"J Franklin Inst"},{"issue":"3","key":"1354_CR13","doi-asserted-by":"publisher","first-page":"412","DOI":"10.1002\/acs.2852","volume":"32","author":"DC Huong","year":"2018","unstructured":"Huong DC, Thuan MV (2018) Design of unknown input reduced-order observers for a class of nonlinear fractional-order time-delay systems. Int J Adapt Control Signal Process 32(3):412\u2013423","journal-title":"Int J Adapt Control Signal Process"},{"key":"1354_CR14","doi-asserted-by":"publisher","first-page":"477","DOI":"10.1177\/0142331216661758","volume":"40","author":"DC Huong","year":"2018","unstructured":"Huong DC (2018) A fresh approach to the design of observers for time-delay systems. Trans Inst Meas Control 40:477\u2013503","journal-title":"Trans Inst Meas Control"},{"key":"1354_CR15","doi-asserted-by":"publisher","first-page":"2802","DOI":"10.1080\/00207721.2019.1690715","volume":"50","author":"DC Huong","year":"2019","unstructured":"Huong DC (2019) Design of functional interval observers for nonlinear fractional-order interconnected systems. Int J Syst Sci 50:2802\u20132814","journal-title":"Int J Syst Sci"},{"key":"1354_CR16","doi-asserted-by":"publisher","first-page":"1389","DOI":"10.1177\/1077546307087442","volume":"14","author":"I Jesus","year":"2008","unstructured":"Jesus I, Machado JAT, Cunha JB (2008) Fractional electrical impedances in botanical elements. J Vib Control 14:1389\u20131402","journal-title":"J Vib Control"},{"key":"1354_CR17","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-20502-6","volume-title":"Selected problems of fractional systems theory","author":"T Kaczorek","year":"2011","unstructured":"Kaczorek T (2011) Selected problems of fractional systems theory. Springer, Berlin"},{"key":"1354_CR18","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-319-11361-6","volume-title":"Fractional linear systems and electrical circuits","author":"T Kaczorek","year":"2015","unstructured":"Kaczorek T, Rogowski K (2015) Fractional linear systems and electrical circuits. Springer, Berlin"},{"key":"1354_CR19","doi-asserted-by":"publisher","first-page":"245","DOI":"10.1515\/amcs-2017-0017","volume":"27","author":"T Kaczorek","year":"2017","unstructured":"Kaczorek T (2017) Reduced-order perfect nonlinear observers of fractional descriptor discrete-time nonlinear systems. Int J Appl Math Comput Sci 27:245\u2013251","journal-title":"Int J Appl Math Comput Sci"},{"key":"1354_CR20","doi-asserted-by":"publisher","first-page":"1489","DOI":"10.1016\/j.nonrwa.2011.11.013","volume":"12","author":"E Kaslik","year":"2012","unstructured":"Kaslik E, Sivasundaram S (2012) Non-existence of periodic solutions in fractional-order dynamical systems and a remarkable difference between integer and fractional-order derivatives of periodic functions. Nonlinear Anal Real World Appl 12:1489\u20131497","journal-title":"Nonlinear Anal Real World Appl"},{"key":"1354_CR21","volume-title":"Theory and application of fractional differential equations","author":"A Kilbas","year":"2006","unstructured":"Kilbas A, Srivastava H, Trujillo J (2006) Theory and application of fractional differential equations. Elsevier, New York"},{"key":"1354_CR22","doi-asserted-by":"publisher","first-page":"1963","DOI":"10.1080\/00207179.2015.1025429","volume":"88","author":"WY Leong","year":"2015","unstructured":"Leong WY, Trinh H, Fernando T (2015) A practical functional observer scheme for interconnected time-delay systems. Int J Control 88:1963\u20131973","journal-title":"Int J Control"},{"key":"1354_CR23","doi-asserted-by":"publisher","first-page":"2482","DOI":"10.1016\/j.jfranklin.2016.04.017","volume":"353","author":"WY Leong","year":"2016","unstructured":"Leong WY, Trinh H, Hien LV (2016) An LMI-based functional estimation scheme of large-scale time-delay systems with strong interconnections. J Franklin Inst 353:2482\u20132510","journal-title":"J Franklin Inst"},{"key":"1354_CR24","doi-asserted-by":"publisher","DOI":"10.1016\/j.neucom.2020.04.083","author":"B Liu","year":"2020","unstructured":"Liu B, Su H, Wu L, Li X, Lu X (2020) Fractional-order controllability of multi-agent systems with time-delay. Neurocomputing. https:\/\/doi.org\/10.1016\/j.neucom.2020.04.083","journal-title":"Neurocomputing"},{"key":"1354_CR25","doi-asserted-by":"publisher","first-page":"27","DOI":"10.1140\/epjst\/e2011-01379-1","volume":"193","author":"CP Li","year":"2011","unstructured":"Li CP, Zhang FR (2011) A survey on the stability of fractional differential equations. Eur Phys J Spec Top 193:27\u201347","journal-title":"Eur Phys J Spec Top"},{"key":"1354_CR26","doi-asserted-by":"publisher","first-page":"74","DOI":"10.1016\/j.ins.2019.04.007","volume":"491","author":"P Mani","year":"2019","unstructured":"Mani P, Rajan R, Shanmugam L, Joo YH (2019) Adaptive control for fractional order induced chaotic fuzzy cellular neural networks and its application to image encryption. Inf Sci 491:74\u201389","journal-title":"Inf Sci"},{"key":"1354_CR27","volume-title":"An introduction to the fractional calculus and fractional differential equation","author":"K Miller","year":"1993","unstructured":"Miller K, Ross B (1993) An introduction to the fractional calculus and fractional differential equation. John Wiley & Sons Inc, New York"},{"key":"1354_CR28","doi-asserted-by":"publisher","first-page":"2744","DOI":"10.1016\/j.sigpro.2006.02.018","volume":"86","author":"RR Nigmatullina","year":"2006","unstructured":"Nigmatullina RR, Nelson SO (2006) Recognition of the fractional kinetics in complex systems: dielectric properties of fresh fruits and vegetables from 0.01 to 1.8 GHz. Signal Process 86:2744\u20132759","journal-title":"Signal Process"},{"key":"1354_CR29","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-18101-6","volume-title":"Fractional-order nonlinear systems","author":"I Petras","year":"2011","unstructured":"Petras I (2011) Fractional-order nonlinear systems. Springer, Berlin"},{"key":"1354_CR30","volume-title":"Fractional differential equations","author":"I Podlubny","year":"1999","unstructured":"Podlubny I (1999) Fractional differential equations. Academic Press, New York"},{"key":"1354_CR31","doi-asserted-by":"publisher","first-page":"1309","DOI":"10.1007\/s00521-016-2641-9","volume":"29","author":"C Rajivganthi","year":"2018","unstructured":"Rajivganthi C, Rihan FA, Lakshmanan S, Muthukumar P (2018) Finite-time stability analysis for fractional-order Cohen-Grossberg BAM neural networks with time delays. Neural Comput Appl 29:1309\u20131320","journal-title":"Neural Comput Appl"},{"key":"1354_CR32","doi-asserted-by":"publisher","first-page":"105344","DOI":"10.1016\/j.cnsns.2020.105344","volume":"90","author":"M Tavazoei","year":"2020","unstructured":"Tavazoei M, Asemani MH (2020) On robust stability of incommensurate fractional-order systems. Commun Nonlinear Sci Numer Simul 90:105344","journal-title":"Commun Nonlinear Sci Numer Simul"},{"key":"1354_CR33","doi-asserted-by":"publisher","first-page":"1411","DOI":"10.1016\/j.jfranklin.2017.12.030","volume":"355","author":"H Trinh","year":"2018","unstructured":"Trinh H, Huong DC (2018) A new method for designing distributed reduced-order functional observers of interconnected time-delay systems. J Franklin Inst 355:1411\u20131451","journal-title":"J Franklin Inst"},{"key":"1354_CR34","doi-asserted-by":"publisher","first-page":"378","DOI":"10.1177\/0142331218757864","volume":"41","author":"H Trinh","year":"2019","unstructured":"Trinh H, Huong DC, Nahavandi S (2019) Observers design for positive fractional-order interconnected time-delay systems. Trans Inst Meas Control 41:378\u2013391","journal-title":"Trans Inst Meas Control"},{"key":"1354_CR35","doi-asserted-by":"publisher","first-page":"1015","DOI":"10.1007\/s11071-015-2214-y","volume":"85","author":"Y Wen","year":"2015","unstructured":"Wen Y, Zhou XF, Zhang Z, Liu S (2015) Lyapunov method for nonlinear fractional differential systems with delay. Nonlinear Dyn 85:1015\u20131025","journal-title":"Nonlinear Dyn"},{"key":"1354_CR36","doi-asserted-by":"publisher","first-page":"1572","DOI":"10.1016\/j.matcom.2012.01.004","volume":"82","author":"Y Yan","year":"2012","unstructured":"Yan Y, Kou C (2012) Stability analysis for a fractional differential model of HIV infection of CD4$$^+$$ T-cells with time delay. Math Comput Simul 82:1572\u20131585","journal-title":"Math Comput Simul"},{"key":"1354_CR37","doi-asserted-by":"publisher","DOI":"10.1177\/0959651820945828","author":"DTH Yen","year":"2020","unstructured":"Yen DTH, Huong DC (2020) Functional interval observers for nonlinear fractional-order systems with time-varying delays and disturbances. Proc Inst Mech Eng. https:\/\/doi.org\/10.1177\/0959651820945828","journal-title":"Proc Inst Mech Eng"},{"key":"1354_CR38","doi-asserted-by":"publisher","first-page":"193","DOI":"10.1016\/j.sysconle.2005.07.002","volume":"55","author":"B Zhou","year":"2006","unstructured":"Zhou B, Duan GR (2006) A new solution to the generalized Sylvester matrix equation $$AV-EVF=BW$$. Syst Control Left. 55:193\u2013198","journal-title":"Syst Control Left."}],"container-title":["Computational and Applied Mathematics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s40314-020-01354-w.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s40314-020-01354-w\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s40314-020-01354-w.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,10,25]],"date-time":"2023-10-25T17:55:50Z","timestamp":1698256550000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s40314-020-01354-w"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,10,15]]},"references-count":38,"journal-issue":{"issue":"4","published-print":{"date-parts":[[2020,12]]}},"alternative-id":["1354"],"URL":"https:\/\/doi.org\/10.1007\/s40314-020-01354-w","relation":{},"ISSN":["2238-3603","1807-0302"],"issn-type":[{"type":"print","value":"2238-3603"},{"type":"electronic","value":"1807-0302"}],"subject":[],"published":{"date-parts":[[2020,10,15]]},"assertion":[{"value":"8 July 2020","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"16 September 2020","order":2,"name":"revised","label":"Revised","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"5 October 2020","order":3,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"15 October 2020","order":4,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}],"article-number":"297"}}