Xu, Honglei; Liu, Xinzhi; Teo, Kok Lay A LMI approach to stability analysis and synthesis of impulsive switched systems with time delays. (English) Zbl 1157.93501 Nonlinear Anal., Hybrid Syst. 2, No. 1, 38-50 (2008). Summary: This paper studies the asymptotic stability problem for a class of impulsive switched systems with time invariant delays based on Linear Matrix Inequality (LMI) approach. Some sufficient conditions, which are independent of time delays and impulsive switching intervals, for ensuring asymptotical stability of these systems are derived by using a Lyapunov-Krasovskii technique. Moreover, some appropriate feedback controllers, which can stabilize the closed-loop systems, are constructed. Illustrative examples are presented to show the effectiveness of the results obtained. Cited in 27 Documents MSC: 93D20 Asymptotic stability in control theory 93B50 Synthesis problems 34A37 Ordinary differential equations with impulses Keywords:linear matrix inequality; impulsive switched system; time delay; asymptotic stability PDFBibTeX XMLCite \textit{H. Xu} et al., Nonlinear Anal., Hybrid Syst. 2, No. 1, 38--50 (2008; Zbl 1157.93501) Full Text: DOI Link References: [1] Ding, X.; Xu, H., Robust stability and stabilization of a class of impulsive switched systems, Dynamics of Continuous Discrete and Impulsive Systems-Series B, 2, 795-798 (2005), (Sp. Iss. SI) [2] C.Y. Wen, Z.G. Li, Y.C. Soh, A unified approach for stability analysis of impulsive hybrid systems, in: Proceedings of the 38th IEEE Conference on Decision and Control, vol. 5, 1999, pp. 4398-4403; C.Y. Wen, Z.G. Li, Y.C. Soh, A unified approach for stability analysis of impulsive hybrid systems, in: Proceedings of the 38th IEEE Conference on Decision and Control, vol. 5, 1999, pp. 4398-4403 [3] Xu, H.; Liu, X.; Teo, K. L., Robust \(H \infty\) stabilization with definite attendance of uncertain impulsive switched systems, Journal of ANZIAM, 46, 471-484 (2005) [4] Hill, D. J.; Guan, Z.; Shen, X., On hybrid impulsive and switching systems and aplication to nonlinear control, IEEE Transactions on Automatic Control, 50, 1058-1062 (2005) · Zbl 1365.93347 [5] Liu, X.; Liu, B.; Liao, X., Stability and robustness of quasi-linear impulsive hybrid systems, Journal of Mathematical Analysis and Applications, 283, 416-430 (2003) · Zbl 1047.93041 [6] Gu, K., Survey on recent results in the stability and control of time delay systems, Journal of Dynamic Systems, Measurement and Control, 125, 158-165 (2003) [7] Li, X.; de Souza, C. E., Delay dependent robust stability and stabilization of uncertain time delay systems: A linear matrix inequality approach, IEEE Transaction of Automatic Control, 42, 1144-1148 (1997) · Zbl 0889.93050 [8] Doyle, J. C.; Zhou, K.; Glover, K., Robust and Optimal Control (1996), Prentice Hall: Prentice Hall NJ · Zbl 0999.49500 [9] Park, P., A delay-dependent stability criterion for systems with uncertain time-invariant delays, IEEE Transaction on Automatic Control, 44, 876-877 (1999) · Zbl 0957.34069 [10] Feron, E.; Boyd, S.; Ghaoui, L. E.; Balakrishnan, V., Linear Matrix Inequalities in System and Control Theory (1994), SIAM: SIAM Philadelphia · Zbl 0816.93004 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.