×
Zhang, Lijun; Zhao, Jiemei

Delay-dependent exponential stability for discrete-time singular switched systems with time-varying delay. (English) Zbl 1327.93332

Asian J. Control 15, No. 2, 630-635 (2013).
Summary: In this paper, the exponential stability problem is investigated for a class of discrete-time singular switched systems with time-varying delay. By using a new Lyapunov functional and average dwell time scheme, a delay-dependent sufficient condition is established in terms of linear matrix inequalities for the considered system to be regular, causal, and exponentially stable. Different from the existing results, in the considered systems the corresponding singular matrices do not need to have the same rank. A numerical example is given to demonstrate the effectiveness of the proposed result.

Cited in 5 Documents

MSC:

93D20 Asymptotic stability in control theory
93C55 Discrete-time control/observation systems
93C30 Control/observation systems governed by functional relations other than differential equations (such as hybrid and switching systems)

Keywords:

delay-dependent; discrete-time singular switched systems; time-varying delay; exponential stability; average dwell time
Cite Review PDF
Full Text: DOI

References:

[1] Hespanha, J. P. and A. S.Morse, “Stability of switched systems with average dwell time,” Proc. 38th IEEE Conf. Decision Control, Phoenix, AZ, pp. 2655-2660 (1999).
[2] Wu, L. and W. X.Zheng, “Weighted H_∞ model reduction for switched hybrid systems with time‐varying delay,” Automatica, Vol. 45, No. 1, pp. 186-193 (2009). · Zbl 1154.93326
[3] Wu, L., Z.Feng, and W.Zheng, “Exponential stability analysis for delayed neural networks with switching parameters: average dwell time approach,” IEEE Trans. Neural Netw., Vol. 21, No. 9, pp. 1396-1407 (2010).
[4] Zhang, L. X., E. K.Boukas, and P.Shi, “Exponential H_∞ filtering for uncertain discrete‐time switched linear systems with average dwell time: A μ‐dependent approach,” Int. J. Robust Nonlinear Control, Vol. 18, No. 11, pp. 1188-1207 (2008). · Zbl 1284.93238
[5] Zhang, W. A. and L.Yu, “Stability analysis for discrete‐time switched time‐delay system,” Automatica, Vol. 45, No. 10, pp. 2265-2271 (2009). · Zbl 1179.93145
[6] Dai, L., Singular Control Systems, Lecture Notes in Control and Information Sciences, New York: Springer‐Verlag (1989). · Zbl 0669.93034
[7] Wu, L. and D. W. C.Ho, “Sliding mode control of singular stochastic hybrid systems,” Automatica, Vol. 46, No. 4, pp. 779-783 (2010). · Zbl 1193.93184
[8] Wu, L., P.Shi, and H.Gao, “State estimation and sliding mode control of markovian jump singular systems,” IEEE Trans. Autom. Control, Vol. 55, No. 5, pp. 1213-1219 (2010). · Zbl 1368.93696
[9] Zhang, X. and H.Zhu, “Robust stability and stabilization criteria for discrete singular time‐delay LPV systems,” Asian J. Control, Vol. 14, No. 4, pp. 1084-1094 (2012). · Zbl 1287.93065
[10] Haidar, A., E. K.Boukas, S.Xu, and J.Lam, “Exponential stability and static output feedback stabilisation of singular timedelay systems with saturating actuators,” IET Control Theory Appl., Vol. 3, No. 9, pp. 1293-1305 (2009).
[11] Lin, J. and S.Fei, “Reliable control for a class of uncertain singular systems with interval time‐varying delay,” Asian J. Control, Vol. 13, No. 4, pp. 542-552 (2011). · Zbl 1219.93105
[12] Meng, B. and F.Zhang, “Reachability conditions for switched linear singular systems,” IEEE Trans. Autom. Control, Vol. 51, No. 3, pp. 482-488 (2006). · Zbl 1366.93059
[13] Ma, S., C.Zhang, and Z.Wu, “Delay‐dependent stability and H_∞ control for uncertain discrete switched singular systems with time‐delay,” Appl. Math. Comput., Vol. 206, No. 1, pp. 413-424 (2008). · Zbl 1152.93461
[14] Zhai, G. and X.Xu, “A unified approach to stability analysis of switched linear descriptor systems under arbitrary switching,” Int. J. Appl. Math. Comput. Sci., Vol. 20, No. 2, pp. 249-259 (2010). · Zbl 1196.93070
[15] Zhai, G., R.Kou, J.Imae, and T.Kobayashi, “Stability analysis and design for switched descriptor systems,” Int. J. Control Autom. Syst., Vol. 7, No. 3, pp. 349-355 (2009).
[16] Zhang, X. and Q.Han, “Delay‐dependent robust H_∞ filtering for uncertain discrete‐time systems with time‐varying delay based on a finite sum inequality,” IEEE Trans. Circuits Syst. II‐Express Briefs, Vol. 53, No. 1, pp. 1446-1470 (2006).
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. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.