zbMATH — the first resource for mathematics

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.

a & b logic and
a | b logic or
!ab logic not
abc* right wildcard
"ab c" phrase
(ab c) parentheses
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)
Delay-dependent stability analysis and synthesis of uncertain T-S fuzzy systems with time-varying delay. (English) Zbl 1082.93031
Summary: This paper considers the delay-dependent stability analysis and controller design for uncertain T-S fuzzy system with time-varying delay. A new method is provided by introducing some free-weighting matrices and employing the lower bound of time-varying delay. Based on the Lyapunov-Krasovskii functional method, sufficient condition for the asymptotical stability of the system is obtained. By constructing the Lyapunov-Krasovskii functional appropriately, we can avoid the supplementary requirement that the time-derivative of time-varying delay must be smaller than one. The fuzzy state feedback gain is derived through the numerical solution of a set of linear matrix inequalities (LMIs). The upper bound of time-delay can be obtained by using convex optimization such that the system can be stabilized for all time-delays. The efficiency of our method is demonstrated by two numerical examples.

93C42Fuzzy control systems
93D05Lyapunov and other classical stabilities of control systems
Full Text: DOI
[1] Cao, Y. -Y.; Frank, P. M.: Analysis and synthesis of nonlinear time-delay systems via fuzzy control approach. IEEE trans. Fuzzy systems 8, No. 2, 200-211 (2000)
[2] Cao, Y. -Y.; Frank, P. M.: Stability analysis and synthesis of nonlinear time-delay systems via linear Takagi -- sugeno fuzzy models. Fuzzy sets and systems 124, 213-229 (2001) · Zbl 1002.93051
[3] Chang, W. -J.; Chang, W.: Fuzzy control of continuous time-delay affine T -- S fuzzy systems. Proceedings of the 2004 IEEE internat. Conf. on networking, sensing and control Taipei, 618-623 (2004)
[4] Chen, B.; Liu, X. P.: Reliable control design of fuzzy dynamic systems with time-varying delay. Fuzzy sets and systems 146, 349-374 (2004) · Zbl 1055.93050
[5] Fridman, E.: New Lyapunov -- Krasovskiĭ functionals for stability of linear retarded and neutral type systems. Systems control lett. 43, 309-319 (2001) · Zbl 0974.93028
[6] Gu, K.; Kharitonov, V. L.; Chen, J.: Stability of time-delay systems. (2003) · Zbl 1039.34067
[7] Guan, X. P.; Chen, C. L.: Delay-dependent guaranteed cost control for T -- S fuzzy systems with time delays. IEEE trans. Fuzzy systems 12, 236-249 (2004) · Zbl 1142.93363
[8] 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 trans. Automat. control 49, No. 5, 828-832 (2004)
[9] Lee, K. R.; Kim, J. H.; Jeung, E. T.; Park, H. B.: Output feedback robust H$\infty $ control of uncertain fuzzy dynamic system with time-varying delay. IEEE trans. Fuzzy systems 8, No. 6, 657-664 (2000)
[10] Li, C. G.; Wang, H. J.; Liao, X. F.: Delay-dependent robust stability of uncertain fuzzy systems with time varying delays. IEE proc.-control theory appl. 151, 417-421 (2004)
[11] M. Li, H.G. Zhang, Fuzzy H\infty  robust control for nonlinear time-delay system via fuzzy performance evaluator, IEEE Internat. Conf. on Fuzzy Systems, 2003, pp. 555 -- 560.
[12] Moon, Y. S.; Park, P.; Kwon, W. H.: Delay-dependent robust stabilization of uncertain state-delayed systems. Internat. J. Control 74, No. 14, 1447-1455 (2001) · Zbl 1023.93055
[13] Moon, Y. S.; Park, P.; Kwon, W. H.: Robust stabilization of uncertain input-delayed systems using reduction method. Automatica 37, 307-312 (2001) · Zbl 0969.93035
[14] Niculescu, S. -I.: On delay-dependent stability under model transformation of some neutral linear systems. Internat. J. Control 74, No. 6, 609-617 (2001) · Zbl 1047.34088
[15] Takagi, T.; Sugeno, M.: Fuzzy identification of its applications to modeling and control. IEEE trans. Systems man cybernet., 116-132 (1985) · Zbl 0576.93021
[16] Wang, R. J.; Lin, W. W.; Wang, W. J.: Stabilizability of linear quadratic state feedback for uncertain fuzzy time-delay systems. IEEE trans. Systems man cybernet. (Part B) 34, 1288-1292 (2004)
[17] Wu, M.; He, Y.; She, J. H.: New delay-dependent stability criteria and stabilizing method for neutral systems. IEEE trans. Autom. control 49, No. 12, 2266-2271 (2004)
[18] Yoneyama, J.: Robust control analysis and synthesis for uncertain fuzzy systems with time-delay. IEEE trans. Fuzzy systems, 396-401 (2003)
[19] Yue, D.; Han, Q. -L.: Delay-dependent exponential stability of stochastic systems with time-varying delay, nonlinearity and Markovian switching. IEEE trans. Automat. control 50, 217-222 (2005)
[20] Yue, D.; Han, Q. -L.: Delayed feedback control of uncertain systems with time-varying input delay. Automatica 2, 233-240 (2005) · Zbl 1072.93023
[21] Yue, D.; Lam, J.: Reliable memory feedback design for a class of non-linear time delay systems. Internat. J. Robust and nonlinear control 14, 39-60 (2004) · Zbl 1036.93056
[22] Yue, D.; Won, S.: Delay-dependent robust stability of stochastic systems with time delay and nonlinear uncertainties. Electronics lett. 37, No. 15, 992-993 (2001) · Zbl 1190.93095
[23] Yue, D.; Won, S.: An improvement on ”delay and its time-derivative-dependent robust stability of time-delayed linear systems with uncertainty”. IEEE trans. Automat. control 47, No. 2, 407-408 (2002)
[24] D. Yue, S. Won, Delay-dependent exponential stability of a class of neutral systems with time delay and time-varying parameter uncertainties: an LMI approach, JSME Internat. Journal (Part C) (1) (2003) 245 -- 251.
[25] Yue, D.; Won, S.: Delay-dependent stability of neutral systems with time delay: LMI approach. IEE proc.-control theory appl. 150, No. 1, 23-27 (2003)
[26] Zhang, Y.; Pheng, A. H.: Stability of fuzzy control systems with bounded uncertain delays. IEEE trans. Fuzzy systems 10, No. 1, 92-97 (2002) · Zbl 1142.93377