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 robust $H _{\infty }$ admissibility and stabilization for uncertain singular system with Markovian jumping parameters. (English) Zbl 1169.93420
Summary: This paper investigates the problem of delay-dependent robust $H _{\infty }$ admissibility and stabilization for uncertain singular time delay systems with Markovian jumping parameters. The considered systems are not necessarily assumed to be regular and impulse-free. In terms of the linear matrix inequality approach, a delay-dependent stochastic admissibility criterion is given to ensure that the nominal system is regular, impulse-free and stochastically stable. Based on this criterion, the problem is solved. A numerical example is provided to demonstrate the efficiency of the proposed methods in this paper.

93E15Stochastic stability
60J75Jump processes
93C41Control problems with incomplete information
15A39Linear inequalities of matrices
Full Text: DOI
[1] E.K. Boukas, On robust stability of singular systems with random abrupt changes. Nonlinear Anal. Theory Methods Appl. 63, 301--310 (2005) · Zbl 1089.34046 · doi:10.1016/j.na.2005.03.110
[2] E.K. Boukas, Stabilization of stochastic singular nonlinear hybrid systems. Nonlinear Anal. 64, 217--228 (2006) · Zbl 1090.93048 · doi:10.1016/j.na.2005.05.066
[3] E.K. Boukas, S. Xu, J. Lam, On stability and stabilizability of singular stochastic systems with delays. J. Optim. Theory Appl. 127, 249--262 (2005) · Zbl 1101.93077 · doi:10.1007/s10957-005-6538-5
[4] Y.Y. Cao, J. Lam, Robust H control of uncertain Markovian jump systems with time-delay. IEEE Trans. Autom. Control 45, 77--85 (2000) · Zbl 0983.93075 · doi:10.1109/9.827358
[5] W.H. Chen, J.X. Xu, Z.H. Guan, Guaranteed cost control for uncertain Markovian jump systems with mode-dependent time-delays. IEEE Trans. Autom. Control 48, 2270--2277 (2003) · doi:10.1109/TAC.2003.820165
[6] W.H. Chen, Z.H. Guan, X. Lu, Delay-dependent output feedback stabilisation of Markovian jump system with time-delay. IEE Proc. Control Theory Appl. 151, 561--566 (2004) · doi:10.1049/ip-cta:20040844
[7] W.H. Chen, Z.H. Guan, P. Yu, Delay-dependent stability and H control of uncertain discrete-time Markovian jump systems with mode-dependent time delays. Syst. Control Lett. 52, 361--376 (2004) · Zbl 1157.93438 · doi:10.1016/j.sysconle.2004.02.012
[8] W.H. Chen, Z.H. Guan, X. Lu, Passive control synthesis for uncertain Markovian jump systems with multiple mode-dependent time-delays. Asian J. Control 7, 135--143 (2005) · doi:10.1111/j.1934-6093.2005.tb00382.x
[9] L. Dai, Singular Control Systems (Springer, Berlin, 1989) · Zbl 0669.93034
[10] Y.M. Fu, G.R. Duan, Robust guaranteed cost observer for uncertain descriptor time-delay systems with Markovian jumping parameters. Acta Autom. Sinica 31, 479--483 (2005)
[11] Y.M. Fu, G.R. Duan, Q. Lei, Robust guaranteed cost observer design for uncertain descriptor systems with state delays and Markovian jumping parameters. Int. J. Math. Control Inf. 23, 403--412 (2006) · Zbl 1113.93044
[12] Z.W. Gao, S.X. Ding, Actuator fault robust estimation and fault-tolerant control for a class of nonlinear descriptor systems. Automatica 43, 912--920 (2007) · Zbl 1117.93019 · doi:10.1016/j.automatica.2006.11.018
[13] Z.W. Gao, S.X. Ding, Fault estimation and fault-tolerant control for descriptor systems via proportional, multiple-integral and derivative observer design. IET Control Theory Appl. 1, 1208--1218 (2007) · doi:10.1049/iet-cta:20060389
[14] Y. He, Q.-G. Wang, L. Xie, C. Lin, Further inprovement of free-weighting matrices technique for systems with time-varying delay. IEEE Trans. Autom. Control 52, 293--299 (2007) · doi:10.1109/TAC.2006.887907
[15] J. Lam, Z. Shu, S. Xu, E.-K. Boukas, Robust H control of descriptor discrete-time Markovian jump systems. Int. J. Control 80, 374--385 (2007) · Zbl 1120.93057 · doi:10.1080/00207170600999322
[16] C. Lin, Q.-G. Wang, T.H. Lee, Robust normalization and stabilization of uncertain descripter systems with norm-bounded perturbations. IEEE Trans. Autom. Control 50, 515--520 (2005) · doi:10.1109/TAC.2005.844908
[17] X. Mao, Exponential stability of stochastic delay internal systems with Markovian switching. IEEE Trans. Autom. Control 47, 1604--1612 (2002) · doi:10.1109/TAC.2002.803529
[18] X. Mao, J. Lam, S. Xu, H. Gao, Razumikhin method and exponential stability of hybrid stochastic delay interval systems. J. Math. Anal. Appl. 314, 45--66 (2006) · Zbl 1127.60072
[19] Z. Wang, D.W.C. Ho, Filtering on nonlinear time-delay stochastic systems. Automatica 39, 101--109 (2003) · Zbl 1010.93099 · doi:10.1016/S0005-1098(02)00178-4
[20] Z. Wang, H. Qiao, K.J. Burnham, On stabilization of bilinear uncertain time-delay stochastic systems with Markovian jumping parameters. IEEE Trans. Autom. Control 47, 640--646 (2002) · doi:10.1109/9.995042
[21] Z. Wang, Y. Liu, L. Yu, X. Liu, Exponential stability of delayed recurrent neural networks with Markovian jumping parameters. Phys. Lett. A 356, 346--352 (2006) · Zbl 1160.37439 · doi:10.1016/j.physleta.2006.03.078
[22] Z. Wang, J. Lam, X. Liu, Filtering for a class of nonlinear discrete-time stochastic systems with state delays. J. Comput. Appl. Math. 210, 153--163 (2007) · Zbl 1152.93053 · doi:10.1016/j.cam.2006.02.009
[23] Z. Wang, S. Lauria, J. Fang, X. Liu, Exponential stability of uncertain stochastic neural networks with mixed time-delays. Chaos Solitons Fractals 32, 62--72 (2007) · Zbl 1152.34058 · doi:10.1016/j.chaos.2005.10.061
[24] Z. Wang, F. Yang, D.W.C. Ho, X. Liu, Robust variance-constrained H control for stochastic systems with multiplicative noises. J. Math. Anal. Appl. 328, 487--502 (2007) · Zbl 1117.93068 · doi:10.1016/j.jmaa.2006.05.067
[25] G. Wei, Z. Wang, H. Shu, K. Fraser, X. Liu, Robust filtering for gene expression time series data with variance constraints. Int. J. Comput. Math. 84, 619--633 (2007) · Zbl 1116.62100 · doi:10.1080/00207160601134433
[26] G. Wei, Z. Wang, H. Shu, Nonlinear H control of stochastic time-delay systems with Markovian switching. Chaos Solitons Fractals 35, 442--451 (2008) · Zbl 1138.93061 · doi:10.1016/j.chaos.2006.05.015
[27] Z. Wu, W. Zhou, Delay-dependent robust H control for uncertain singular time-delay systems. IET Control Theory Appl. 1, 1234--1241 (2007) · doi:10.1049/iet-cta:20060446
[28] M. Wu, Y. He, J.-H. She, G.-P. Liu, Delay-dependent criteria for robust stability of time-varying delay systems. Automatica 40, 1435--1439 (2004) · Zbl 1059.93108 · doi:10.1016/j.automatica.2004.03.004
[29] L. Xie, C.E. Souza, Robust H control for linear systems with norm-bounded time-varying uncertainties. IEEE Trans. Autom. Control 14, 1188--1191 (1992) · Zbl 0764.93027 · doi:10.1109/9.151101
[30] J. Xiong, J. Lam, H. Gao, D.W.C. Ho, On robust stabilization of Markovian jump systems with uncertain switching probabilities. Automatica 41, 897--903 (2005) · Zbl 1093.93026 · doi:10.1016/j.automatica.2004.12.001
[31] S. Xu, J. Lam, Robust Control and Filtering of Singular Systems (Springer, Berlin, 2006) · Zbl 1114.93005
[32] S. Xu, C. Yang, H state feedback control for discrete singular systems. IEEE Trans. Autom. Control 45, 1405--1409 (2000) · Zbl 0990.93018 · doi:10.1109/9.880625