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)
Nonfragile observer for discrete-time switched nonlinear systems with time delay. (English) Zbl 1205.94147
Summary: This paper investigates the problem of the nonfragile observer design for discrete-time switched nonlinear systems with time delay. Based on the average dwell-time approach and linear matrix inequality (LMI) techniques, an exponential stability criterion for the discrete-time switched delay system with Lipschitz nonlinearity is derived. Based on several technical lemmas, the discrete-time observer design can be transferred to the problem of solving a set of LMIs. Furthermore, in cases when the gain of the state observer varies, a kind of nonfragile observer is proposed, and the solution to the observer gain is also obtained by solving a set of LMIs. Finally, a numerical example is given to illustrate the effectiveness of the proposed method.

94C30Applications of design theory to circuits and networks
93D10Popov-type stability of feedback systems
Full Text: DOI
[1] A. Alessandri, P. Coletta, Switching observers for continuous-time and discrete-time linear systems, in Proceedings of the American Control Conference, Arlington, Virginia, 2516--2521 (2001)
[2] S.P. Boyd, L.E. Ghaoui, E. Feron, V. Balakrishnan, Linear Matrix Inequalities in System and Control Theory (SIAM, Philadelphia, 1994) · Zbl 0816.93004
[3] C.T. Chen, Linear System Theory and Design (Holt, Rinehart and Winston, New York, 1984)
[4] D. Cheng, L. Guo, Y. Lin, Y. Wang, Stabilization of switched linear systems. IEEE Trans. Autom. Control 50(5), 661--666 (2005) · doi:10.1109/TAC.2005.846594
[5] J.P. Hespanha, Uniform stability of switched linear systems: extension of LaSalle’s invariance principle. IEEE Trans. Autom. Control 49(4), 470--482 (2004) · doi:10.1109/TAC.2004.825641
[6] J.P. Hespanha, D. Liberzon, D. Angeli, E.D. Sontag, Nonlinear norm-observability notions and stability of switched systems. IEEE Trans. Autom. Control 50(2), 154--168 (2005) · doi:10.1109/TAC.2004.841937
[7] A.L. Juloski, W.P.M.H. Heemels, S. Weiland, Observer design for a class of piecewise affine systems, in Proceedings of the 41st IEEE Conference on Decision and Control, Las Vegas, Nevada, USA, 2606--2611 (2002) · Zbl 1127.93312
[8] Q.K. Li, J. Zhao, G.M. Dimirovski, Tracking control for switched time-varying delays systems with stabilizable and unstabilizable subsystems. Nonlinear Anal., Hybrid Syst. 3(2), 133--142 (2009) · Zbl 1166.93325 · doi:10.1016/j.nahs.2008.11.004
[9] H. Lin, P.J. Antsaklis, Stability and stabilizability of switched linear systems: a survey of recent results. IEEE Trans. Autom. Control 54(2), 308--322 (2009) · doi:10.1109/TAC.2008.2012009
[10] A.E. Pearson, Y.A. Fiagbedzi, An observer for time lag systems. IEEE Trans. Autom. Control 34(8), 775--777 (1989) · Zbl 0687.93011 · doi:10.1109/9.29412
[11] S. Pettersson, Observer design for switched systems using multiple quadratic Lyapunov functions, in Proceedings of the 2005 IEEE International Symposium on Intelligent Control, pp. 262--267 (2005)
[12] Y. Song, J. Fan, M. Fei, T. Yang Robust, H control of discrete switched system with time delay. Appl. Math. Comput. 205(1), 159--169 (2008) · Zbl 1152.93490 · doi:10.1016/j.amc.2008.05.046
[13] Z. Sun, A robust stabilizing law for switched linear systems. Int. J. Control 77(4), 389--398 (2004) · Zbl 1059.93121 · doi:10.1080/00207170410001667468
[14] Z. Sun, S.S. Ge, Analysis and synthesis of switched linear control systems. Automatica 41(2), 181--195 (2005) · Zbl 1100.93523 · doi:10.1016/j.automatica.2005.06.014
[15] V. Sundarapandian, General observers for discrete-time nonlinear systems. Math. Comput. Model. 39(1), 87--96 (2004) · Zbl 1100.93009 · doi:10.1016/S0895-7177(04)90508-0
[16] R. Wang, J. Zhao, Guaranteed cost control for a class of uncertain switched delay systems: an average dwell-time method. Cybern. Syst. 38(1), 105--122 (2007) · Zbl 1111.93016 · doi:10.1080/01969720600998660
[17] Z. Xiang, R. Wang, Non-fragile observer design for nonlinear switched systems with time delay. Int. J. Intell. Comput. Cybern. 2(1), 175--189 (2009) · Zbl 1183.93080 · doi:10.1108/17563780910939291
[18] Z.R. Xiang, W.M. Xiang, Observer design for a class of switched nonlinear systems. Control Intell. Syst. 36(4), 318--322 (2008) · Zbl 1173.93007
[19] Z.R. Xiang, W.M. Xiang, Stability analysis of switched systems under dynamical dwell time control approach. Int. J. Syst. Sci. 40(4), 347--355 (2009) · Zbl 1172.93391 · doi:10.1080/00207720802436240
[20] D. Xie, L. Wang, F. Hao, Robust stability analysis and control synthesis for discrete-time uncertain switched systems, in Proceedings of Conference Decision and Control, pp. 4812--4817 (2003)
[21] G.S. Zhai, B. Hu, K. Yasuda, A.N. Michel, Disturbance attenuation properties of time-controlled switched systems. J. Franklin Inst. 338(7), 765--779 (2001) · Zbl 1022.93017 · doi:10.1016/S0016-0032(01)00030-8