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Tytuł artykułu

Stability analysis and design of state estimated controller for delay fuzzy systems with parameter

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Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
This paper deals with the problem of stabilization by an estimated state feedback for a family of nonlinear time-delay Takagi-Sugeno fuzzy parameterized systems. The delay is supposed to be constant where the parameter-dependent controls laws are used to compensate the nonlinearities which are formulated in terms of linear matrix inequalities (LMIs). Based on the Lyapunov-Krasovskii functionals, global exponential stability of the closed-loop systems is achieved. The controller and observer gains are able to be separately designed even in the presence of modeling uncertainty and state delay. Finally, a numerical example is given to show the applicability of the main result.
Słowa kluczowe
Rocznik
Strony
709--731
Opis fizyczny
Bibliogr. 25 poz., rys., wzory
Twórcy
  • University of Sfax, IPEIS Sfax, Tunisia
  • University of Sfax, Faculty of Sciences of Sfax, Tunisia
  • University of Artois, Bethune France
Bibliografia
  • [1] N.A. Baleghi and M.H. Shafiei: An observer-based controller design for nonlinear discrete-time switched systems with time-delay and affine parametric uncertainty. Archives of Control Sciences, 30(3), (2020), 501-521. DOI: 10.24425/acs.2020.134675.
  • [2] A. B. Abdallah, I. Ellouze, and M.A. Hammami: Practical stability of nonlinear time-varying cascade systems. Journal of Dynamical and Control Systems, 15 (2009), 45-62. DOI: 10.1007/s10883-008-9057-5.
  • [3] A. Benabdallah, I. Ellouze, and M.A. Hammami: Practical exponential stability of perturbed triangular systems and a separation principle. Asian Journal of Control, 13(3), (2011), 445-448. DOI: 10.1002/asjc.325.
  • [4] B.B. Hamed, I. Ellouze, and M.A. Hammami: Practical uniform stability of nonlinear differential delay equations. Mediterranean Journal of Mathematics, 6 (2010), 139-150. DOI: 10.1007/s00009-010-0083-7.
  • [5] B.B. Hamed and M.A. Hammami: Practical stabilisation of a class of uncertain time-varying nonlinear delay systems. Journal of Control Theory and Applications, 7 (2009), 175-180. DOI: 10.1007/s11768-009-8017-2.
  • [6] J. Dong and G.H. Yang: Dynamic output feedback control synthesis for continuous-time T-S fuzzy systems via a switched fuzzy control scheme. IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics), 38(4), (2008), 1166-1175. DOI: 10.1109/TSMCB.2008.923530.
  • [7] T. Caraballo, M.A. Hammami, and L. Mchiri: Practical stability of stochastic delay evolution equations. Acta Applicandae Mathematicae, 142 (2016), 91-105. DOI: 10.1007/s10440-015-0016-3.
  • [8] J. Duda: Lyapunov matrices approach to the parametric optimization of a system with two delay sand a PD-controller. Archives of Control Sciences, 28(4), (2018), 585-600. DOI: 10.24425/acs.2018.125484.
  • [9] J.K. Hale and S.M. Lunel: Introduction to functional differential equations. Applied Math Sciences. New York: Springer-Verlag, 1991.
  • [10] N. Hadj Taieb, M.A. Hammami, and F. Delmotte: A separation principle for Takagi-Sugeno control fuzzy systems. Archives of Control Sciences, 29(2), (2019), 227-245. DOI: 10.24425/acs.2019.129379.
  • [11] N. Hadj Taieb, M.A. Hammami, and F. Delmotte: Stabilization of a certain class of fuzzy control systems with uncertainties. Archives of Control Sciences, 27(3), (2017), 453-481. DOI: 10.1515/acsc-2017-0028.
  • [12] D. Huang and S.K. Nguang: Robust 𝐻∞ static output feedback control of fuzzy systems: an ILMI approach. IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics), 36(1), (2006), 216-222. DOI: 10.3182/20050703-6-CZ-1902.00538.
  • [13] H. Khalil: Nonlinear Systems. Third ed. Prentice-Hall, Englewood Cliffs, NJ, 2002.
  • [14] D. Krokavec and A. Filasova: LMI based fuzzy observer design for Takagi-Sugeno models containing vestigial nonlinear terms. Archives of Control Sciences, 24(1), (2014), 39-52. DOI: 10.2478/acsc-2014-0003.
  • [15] O. Lamrabeta, A. Ech-Charqya, E.H. Tissira, and F.E. Haoussi: Sampled data control for Takagi-Sugeno fuzzy systems with actuator saturation. Procedia Computer Science, 148 (2019), 448-454. DOI: 10.1016/j.procs.2019.01.057.
  • [16] A. Larrache, M. Lhous, S.B. Rhila, M. Rachik, and A. Tridane: An output sensitivity problem for a class of linear distributed systems with uncertain initial state. Archives of Control Sciences, 30(1), (2020), 139-155. DOI: 10.24425/acs.2020.132589.
  • [17] H.J. Lee, J.B. Park, and G. Chen: Robust fuzzy control of nonlinear systems with parameter uncertainties. IEEE Transactions on Fuzzy Systems, 9 (2001), 369-379. DOI: 10.1109/91.919258.
  • [18] J.C. Lo and M.L. Lin: Observer-based robust 𝐻∞ control for fuzzy systems using two-step procedure. IEEE Transactions on Fuzzy Systems, 12(3), (2004), 350-359. DOI: 10.1109/TFUZZ.2004.825992.
  • [19] X.J. Ma and Z.Q. Sun: Analysis and design of fuzzy reduced-dimentionalm observer and fuzzy functional observer. Fuzzy Sets and Systems, 120 (2001), 35-63. DOI: 10.1016/S0165-0114(99)00145-1.
  • [20] X. Nian and J. Feng: Guaranteed-cost control of a linear uncertain system with multiple time-varying delays: an LMI approach. IEE Proceedings D (Control Theory and Applications), 150(1), (2003), 17-22. DOI: 10.1049/ip-cta:20045104.
  • [21] O. Naifar, A. Ben Makhlouf, and M.A. Hammami: On observer design for a class of nonlinear systems including unknown time-delay. Mediterranean Journal of Mathematics, 13 (2016), 28-41. DOI: 10.1007/s00009-015-0659-3.
  • [22] J. Park, J. Kim, and D. Park: LMI-based design of stabilizing fuzzy controllers for nonlinear systems described by Takagi-Sugeno fuzzy model. Fuzzy Sets and Systems, 122 (2003), 73-82. DOI: 10.1016/S0165-0114(00)00050-6.
  • [23] P. Pepe and I. Karafyllis: Converse Lyapunov-Krasovskii theorems for systems described by neutral functional differential equations in Hale’s form. International Journal of Control, 86(2), (2013), 232-243. DOI: 10.1080/00207179.2012.723137.
  • [24] C.S. Tseng, B.S. Chen, and H.J. Uang: Fuzzy tracking control design for nonlinear dynamics systems via T-S fuzzy model. IEEE Transactions on Fuzzy Systems, 9(3), (2001), 381-392. DOI: 10.1109/91.928735.
  • [25] S. Wangrat and P. Niamsup: Exponentially practical stability of discrete time singular system with delay and disturbance. Advances in Difference Equations, (2018), 1-23. DOI: 10.1186/s13662-018-1570-6.
Uwagi
Opracowanie rekordu ze środków MEiN, umowa nr SONP/SP/546092/2022 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2022-2023)
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-1643c5d4-5d59-492b-8866-aa01370d738d
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