×
Zhao, Ming; Wang, Yueying; Zhou, Pingfang; Duan, Dengping

Stability criteria for singular stochastic hybrid systems with mode-dependent time-varying delay. (English) Zbl 1406.93382

Abstr. Appl. Anal. 2014, Article ID 409819, 9 p. (2014).
Summary: This paper provides a delay-dependent criterion for a class of singular stochastic hybrid systems with mode-dependent time-varying delay. In order to reduce conservatism, a new Lyapunov-Krasovskii functional is constructed by decomposing the delay interval into multiple subintervals. Based on the new functional, a stability criterion is derived in terms of strict linear matrix inequality (LMI), which guarantees that the considered system is regular, impulse-free, and mean-square exponentially stable. Numerical examples are presented to illustrate the effectiveness of proposed method.

MSC:

93E15 Stochastic stability in control theory
93C30 Control/observation systems governed by functional relations other than differential equations (such as hybrid and switching systems)

Keywords:

stability of stochastic hybrid systems; time-varying delay
PDF BibTeX XML Cite
\textit{M. Zhao} et al., Abstr. Appl. Anal. 2014, Article ID 409819, 9 p. (2014; Zbl 1406.93382)
Full Text: DOI

References:

[1] Krasovskii, N. N.; Lidskiĭ, È. A., Analytical design of controllers in systems with random attributes. I. Statement of the problem, method of solving, Automation and Remote Control, 22, 1021-1025 (1961) · Zbl 0104.36704
[2] Shi, P.; Xia, Y.; Liu, G. P.; Rees, D., On designing of sliding-mode control for stochastic jump systems, IEEE Transactions on Automatic Control, 51, 1, 97-103 (2006) · Zbl 1366.93682
[3] Shu, Z.; Lam, J.; Xu, S., Robust stabilization of Markovian delay systems with delay-dependent exponential estimates, Automatica, 42, 11, 2001-2008 (2006) · Zbl 1113.60079
[4] Gao, H. J.; Fei, Z. Y.; Lam, J.; Du, B. Z., Further results on exponential estimates of Markovian jump systems with mode-dependent time-varying delays, IEEE Transactions on Automatic Control, 56, 1, 223-229 (2011) · Zbl 1368.93679
[5] Wu, Z. G.; Shi, P.; Su, H. Y.; Chu, J., Stochastic synchronization of Markovian jump neural netwroks with time-varying delay using sampled-data, IEEE Transactions on Cybernetics, 43, 6, 1796-1896 (2013)
[6] Wu, Z. G.; Shi, P.; Su, H. Y.; Chu, J., Passivity analysis for discrete-time stochastic markovian jump neural networks with mixed time delays, IEEE Transactions on Neural Networks, 22, 10, 1566-1575 (2011)
[7] Xia, Y.; Boukas, E. K.; Shi, P.; Zhang, J., Stability and stabilization of continuous-time singular hybrid systems, Automatica, 45, 6, 1504-1509 (2009) · Zbl 1166.93365
[8] Wu, Z. G.; Su, H. Y.; Chu, J., Delay-dependent \(H_\infty\) control for singular Markovian jump systems with time delay, Optimal Control Applications & Methods, 30, 5, 443-461 (2009)
[9] Wu, L. G.; Shi, P.; Gao, H. J., State estimation and sliding-mode control of Markovian jump singular systems, IEEE Transactions on Automatic Control, 55, 5, 1213-1219 (2010) · Zbl 1368.93696
[10] Zhang, J.; Xia, Y.; Boukas, E. K., New approach to \(H_\infty\) control for Markovian jump singular systems, IET Control Theory & Applications, 4, 11, 2273-2284 (2010)
[11] Mao, X.; Yuan, C., Stochastic Differential Equations with Markovian Switching (2006), London, UK: Imperial College Press, London, UK · Zbl 1126.60002
[12] Mao, X., Exponential stability of stochastic delay interval systems with Markovian switching, IEEE Transactions on Automatic Control, 47, 10, 1604-1612 (2002) · Zbl 1364.93685
[13] Yue, D.; Han, Q. L., Delay-dependent exponential stability of stochastic systems with time-varying delay, nonlinearity, and Markovian switching, IEEE Transactions on Automatic Control, 50, 2, 217-222 (2005) · Zbl 1365.93377
[14] Mao, X.; Shaikhet, L., Delay-dependent stability criteria for stochastic differential delay equations with Markovian switching, Stability and Control, 3, 2, 88-102 (2000)
[15] Yue, D.; Fang, J.; Won, S., Delay-dependent robust stability of stochastic uncertain systems with time delay and Markovian jump parameters, Circuits, Systems, and Signal Processing, 22, 4, 351-365 (2003) · Zbl 1048.93095
[16] Wang, Z. D.; Liu, Y. R.; Liu, X. H., Exponential stabilization of a class of stochastic system with Markovian jump parameters and mode-dependent mixed time-delays, IEEE Transactions on Automatic Control, 55, 7, 1656-1662 (2010) · Zbl 1368.93778
[17] Boukas, E. K., Stabilization of stochastic singular nonlinear hybrid systems, Nonlinear Analysis. Theory, Methods & Applications A, 64, 2, 217-228 (2006) · Zbl 1090.93048
[18] Wu, L. G.; Ho, D. W. C., Sliding mode control of singular stochastic hybrid systems, Automatica, 46, 4, 779-783 (2010) · Zbl 1193.93184
[19] Huang, L. R.; Mao, X. R., Stability of singular stochastic systems with Markovian switching, IEEE Transactions on Automatic Control, 56, 2, 424-429 (2011) · Zbl 1368.93767
[20] Hale, J. K., Theory of Functional Differential Equations (1977), New York, NY, USA: Springer, New York, NY, USA
[21] Gu, K., further refinement of discretized Lyapunov functional method for the stability of time-delay systems, International Journal of Control, 74, 7, 737-744 (2001) · Zbl 1015.34061
[22] Yue, D.; Han, Q. L., Robust \(H_\infty\) filter design of uncertain descriptor systems with discrete and distributed delays, IEEE Transactions on Signal Processing, 52, 11, 3200-3212 (2004) · Zbl 1370.93111
[23] Shu, Z.; Lam, J., Exponential estimates and stabilization of uncertain singular systems with discrete and distributed delays, International Journal of Control, 81, 6, 865-882 (2008) · Zbl 1152.93462
[24] Wang, Y.; Xie, L.; de Souza, C. E., Robust control of a class of uncertain nonlinear systems, Systems & Control Letters, 19, 2, 139-149 (1992) · Zbl 0765.93015
[25] Xu, S.; Lam, J., Robust Control and Filtering of Singular Systems (2006), Berlin, Germany: Springer, Berlin, Germany · Zbl 1114.93005
[26] Boukas, E. K., Stochastic Hybrid Systems: Analysis and Design (2005), Boston, Mass, USA: Birkhäuser Boston, Boston, Mass, USA · Zbl 1085.93026
[27] Mao, X.; Koroleva, N.; Rodkina, A., Robust stability of uncertain stochastic differential delay equations, Systems & Control Letters, 35, 5, 325-336 (1998) · Zbl 0909.93054
[28] Balasubramaniam, P.; Krishnasamy, R.; Rakkiyappan, R., Delay-dependent stability criterion for a class of non-linear singular Markovian jump systems with mode-dependent interval time-varying delays, Communications in Nonlinear Science and Numerical Simulation, 17, 9, 3612-3627 (2012) · Zbl 1351.93163
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.