# zbMATH — the first resource for mathematics

##### Examples
 Geometry Search for the term Geometry in any field. Queries are case-independent. Funct* Wildcard queries are specified by * (e.g. functions, functorial, etc.). Otherwise the search is exact. "Topological group" Phrases (multi-words) should be set in "straight quotation marks". au: Bourbaki & ti: Algebra Search for author and title. The and-operator & is default and can be omitted. Chebyshev | Tschebyscheff The or-operator | allows to search for Chebyshev or Tschebyscheff. "Quasi* map*" py: 1989 The resulting documents have publication year 1989. so: Eur* J* Mat* Soc* cc: 14 Search for publications in a particular source with a Mathematics Subject Classification code (cc) in 14. "Partial diff* eq*" ! elliptic The not-operator ! eliminates all results containing the word elliptic. dt: b & au: Hilbert The document type is set to books; alternatively: j for journal articles, a for book articles. py: 2000-2015 cc: (94A | 11T) Number ranges are accepted. Terms can be grouped within (parentheses). la: chinese Find documents in a given language. ISO 639-1 language codes can also be used.

##### Operators
 a & b logic and a | b logic or !ab logic not abc* right wildcard "ab c" phrase (ab c) parentheses
##### Fields
 any anywhere an internal document identifier au author, editor ai internal author identifier ti title la language so source ab review, abstract py publication year rv reviewer cc MSC code ut uncontrolled term dt document type (j: journal article; b: book; a: book article)
Robust ${H}_{\infty }$ control of Takagi-Sugeno fuzzy systems with state and input time delays. (English) Zbl 1175.93119
Summary: This paper addresses the robust ${H}_{\infty }$ fuzzy control problem for nonlinear uncertain systems with state and input time delays through Takagi-Sugeno (T-S) fuzzy model approach. The delays are assumed to be interval time-varying delays, and no restriction is imposed on the derivative of time delay. Based on Lyapunov-Krasoviskii functional method, delay-dependent sufficient conditions for the existence of an ${H}_{\infty }$ controller are proposed in Linear Matrix Inequality (LMI) format. Illustrative examples are given to show the effectiveness and merits of the proposed fuzzy controller design methodology.
##### MSC:
 93C42 Fuzzy control systems 93B36 ${H}^{\infty }$-control 15A39 Linear inequalities of matrices
##### References:
 [1] Assawinchaichote, W.; Nguang, S. K.; Shi, P.: H$\infty$ output feedback control design for uncertain fuzzy singularly perturbed systems: an lmi approach, Automatica 40, No. 12, 2147-2152 (2004) · Zbl 1059.93504 · doi:10.1016/j.automatica.2004.07.006 [2] Cao, S. G.; Rees, N. W.; Feng, G.: Analysis and design for a class of fuzzy control systems using dynamic fuzzy-state-space models, IEEE trans. Fuzzy systems 7, No. 2, 192-200 (1999) [3] Cao, S. G.; Rees, N. W.; Feng, G.: H$\infty$ control of uncertain fuzzy continuous-time systems, IEEE trans. Fuzzy systems 8, No. 2, 171-190 (2000) · Zbl 0960.93025 · doi:10.1016/S0165-0114(98)00396-0 [4] Cao, Y. Y.; Frank, P. M.: Analysis and synthesis of nonlinear time-delay system via fuzzy control approach, IEEE trans. Fuzzy systems 8, No. 2, 200-211 (2000) [5] Chen, C. L.; Feng, G.; Sun, D.; Zhu, Y.: H$\infty$ output feedback control of discrete-time fuzzy systems with application to chaos control, IEEE trans. Fuzzy systems 13, No. 4, 531-543 (2005) [6] Feng, G.: H$\infty$ controller design of fuzzy dynamic systems based on piecewise Lyapunov functions, IEEE trans. Systems man cybernet. Part B 34, No. 1, 283-292 (2004) [7] Feng, G.: H$\infty$ controller synthesis of fuzzy dynamic systems based on piecewise Lyapunov functions and based on bilinear matrix inequalities, IEEE trans. Fuzzy systems 13, No. 1, 94-103 (2005) [8] Guan, X. P.; Chen, C. L.: Delay-dependent guaranteed cost control for T – S fuzzy systems with time delays, IEEE trans. Fuzzy systems 12, No. 2, 236-249 (2004) · Zbl 1142.93363 · doi:10.1109/TFUZZ.2004.825085 [9] He, Y.; Wu, M.; She, J. H.; Liu, G. P.: Delay-dependent robust stability criteria for uncertain neutral systems with mixed delays, Syst. control lett. 51, No. 1, 57-65 (2004) · Zbl 1157.93467 · doi:10.1016/S0167-6911(03)00207-X [10] He, Y.; Wu, M.; She, J. H.; Liu, G. P.: Parameter-dependent Lyapunov functional for stability of time-delay systems with polytopic-type uncertainties, IEEE transact. Automat. control 49, No. 5, 828-832 (2004) [11] Jang, X.; Han, Q. L.: Robust H$\infty$ control for uncertain t – s fuzzy systems with interval time-varying delay, IEEE trans. Fuzzy systems 15, No. 2, 321-331 (2007) [12] Jiang, X.; Hang, Q. L.; Yu, X. H.: Robust H$\infty$ control for uncertain Takagi – sugeno fuzzy systems with interval time-delay, , 1114-1119 (June 2005) [13] Lee, K. R.; Kim, J. H.; Jeung, E. T.; Park, H. B.: Output feedback robust H$\infty$ control of uncertain fuzzy dynamic systems with time-varying delay, IEEE trans. Fuzzy systems 8, No. 6, 657-664 (2000) [14] Li, G. G.; Wang, M. T.; Liao, X. F.: Delay-dependent robust stability of uncertain fuzzy systems with time-varying delay, IEE proc. Control theory appl. 151, 417-421 (2004) [15] Lin, C.; Wang, Q. G.; Lee, T. H.: Stability and stabilization of a class of fuzzy time-delay descriptor systems, IEEE trans. Fuzzy systems 14, No. 4, 542-551 (2006) [16] Lin, C.; Wang, Q. G.; Lee, T. H.: Delay-dependent LMI conditions for stability and stabilization of T – S fuzzy systems with bounded time-delay, Fuzzy sets and systems 157, 1229-1247 (2006) · Zbl 1090.93024 · doi:10.1016/j.fss.2005.10.001 [17] Lo, J. C.; Lin, M. L.: Observer-based robust H$\infty$ control for fuzzy systems using two-step procedure, IEEE trans. Fuzzy systems 12, No. 3, 350-359 (2004) [18] Moon, Y. S.; Park, P. G.; Kwon, W. H.: Robust stabilization of uncertain input-delayed systems using reduction method, Automatica 37, 307-312 (2001) · Zbl 0969.93035 · doi:10.1016/S0005-1098(00)00145-X [19] Park, J. H.; Kwon, O. M.: Guaranteed cost control of time-delay chaotic systems, Chaos solitons fractals 27, 1011-1018 (2006) · Zbl 1102.37305 · doi:10.1016/j.chaos.2005.04.076 [20] Takagi, T.; Sugeno, M.: Fuzzy identification of systems and its applications to modeling and control, IEEE trans. Systems man cybernet. 15, No. 1, 116-132 (1985) · Zbl 0576.93021 [21] Tanaka, K.; Ikeda, T.; Wang, H. O.: A multiple Lyapunov function approach to stabilization of fuzzy control systems, IEEE trans. Fuzzy systems 11, No. 4, 582-589 (2003) [22] Tanaka, K.; Wang, H. O.: Fuzzy control systems design and analysis. A linear matrix inequality approach, (2001) [23] Tian, E.; Peng, C.: Delay-dependent stabilization analysis and synthesis of uncertain T – S fuzzy systems with time-varying delay, Fuzzy sets and systems 157, 544-559 (2006) · Zbl 1082.93031 · doi:10.1016/j.fss.2005.06.022 [24] Wang, L.; Feng, G.: Piecewise H$\infty$ controller design discrete time fuzzy systems, IEEE trans. Systems man cybernet. Part B 34, No. 1, 682-686 (2004) [25] Wang, Y.; Xie, L.; De Souza, C. E.: Robust control of a class of uncertain nonlinear systems, Systems control lett. 19, 139-149 (1992) · Zbl 0765.93015 · doi:10.1016/0167-6911(92)90097-C [26] Xu, S.; Lam, J.: Robust H-infinity control for uncertain discrete time-delay fuzzy systems via output feedback controllers, IEEE trans. Fuzzy systems 13, No. 1, 82-93 (2005) [27] Xu, S.; Lam, J.: Improved delay-dependent stability criteria for time-delay systems, IEEE trans. Automat. control 50, No. 3, 384-387 (2005) [28] Xu, S.; Lam, J.: On equivalence and efficiency of certain stability criteria for time-delay systems, IEEE trans. Automat. control 52, No. 1, 95-101 (2007) [29] Xu, S.; Lam, J.; Zou, Y.: A simplified descriptor system approach to delay-dependent stability and performance analyses for time-delay systems, IEE proc. Control theory appl. 15, No. 2, 147-151 (2005) [30] Yue, D.; Lam, J.: Delay feedback control of uncertain systems with time-varying input delay, Automatica 41, 233-240 (2005) · Zbl 1072.93023 · doi:10.1016/j.automatica.2004.09.006 [31] Zhang, X. M.; Wu, M.; She, J. H.; He, Y.: Delay-dependent stabilization of linear systems with time-varying state and input delays, Automatica 41, 1405-1412 (2005) [32] Zhang, Y.; Peng, P. Y.; Jiang, Z. P.: Stable neural controller design for unknown nonlinear systems using backstepping, IEEE trans. Neural networks 11, No. 5, 1347-1359 (2000) [33] Zhou, S.; Feng, G.: Generalized H2 controller synthesis for uncertain discrete-time fuzzy systems via basis-dependent Lyapunov functions, IEE proc. Control theory appl. 153, No. 1, 74-78 (2006) [34] Zhou, S. S.; Feng, G.; Lam, J.; Xu, S. Y.: Robust H$\infty$ control for discrete fuzzy systems via basis-dependent Lyapunov functions, Inform. sci. 174, No. 3 – 4, 197-217 (2005) · Zbl 1113.93038 · doi:10.1016/j.ins.2004.07.015