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Cheng, Jun; Zhu, Hong; Zhong, Shouming; Zhang, Yuping

Robust stability of switched delay systems with average dwell time under asynchronous switching. (English) Zbl 1263.93179

J. Appl. Math. 2012, Article ID 956370, 17 p. (2012).
Summary: The problem of robust stability of switched delay systems with average dwell time under asynchronous switching is investigated. By taking advantage of the average dwell-time method and an integral inequality, two sufficient conditions are developed to guarantee the global exponential stability of the considered switched system. Finally, a numerical example is provided to demonstrate the effectiveness and feasibility of the proposed techniques.

Cited in 2 Documents

MSC:

93D09 Robust stability
93C30 Control/observation systems governed by functional relations other than differential equations (such as hybrid and switching systems)

Keywords:

robust stability of switched delay systems; average dwell-time method; global exponential stability
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\textit{J. Cheng} et al., J. Appl. Math. 2012, Article ID 956370, 17 p. (2012; Zbl 1263.93179)
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References:

[1] V. Lakshmikantham, D. D. Baĭnov, and P. S. Simeonov, Theory of Impulsive Differential Equations, World Scientific, Singapore, 1989. · Zbl 0732.34040
[2] S. H. Lee and J. T. Lim, “Stability analysis of switched systems with impulse effects,” in Proceedings of the IEEE International Symposium on Intelligent Control-Intelligent Systems and Semiotics, pp. 79-83, September 1999.
[3] P. Colaneri, J. C. Geromel, and A. Astolfi, “Stabilization of continuous-time switched nonlinear systems,” Systems & Control Letters, vol. 57, no. 1, pp. 95-103, 2008. · Zbl 1129.93042
[4] G. Xie and L. Wang, “Periodic stabilizability of switched linear control systems,” Automatica, vol. 45, no. 9, pp. 2141-2148, 2009. · Zbl 1175.93192
[5] C. Yang and W. Zhu, “Stability analysis of impulsive switched systems with time delays,” Mathematical and Computer Modelling, vol. 50, no. 7-8, pp. 1188-1194, 2009. · Zbl 1185.34109
[6] V. N. Phat, T. Botmart, and P. Niamsup, “Switching design for exponential stability of a class of nonlinear hybrid time-delay systems,” Nonlinear Analysis. Hybrid Systems, vol. 3, no. 1, pp. 1-10, 2009. · Zbl 1157.93500
[7] Z. Xiang, C. Liang, and Q. Chen, “Robust L2-L\infty filtering for switched systems under asynchronous switching,” Communications in Nonlinear Science and Numerical Simulation, vol. 16, no. 8, pp. 3303-3318, 2011. · Zbl 1221.93121
[8] K. Hu and J. Yuan, “Improved robust H\infty filtering for uncertain discrete-time switched systems,” IET Control Theory & Applications, vol. 3, no. 3, pp. 315-324, 2009.
[9] C. S. Tseng and B. S. Chen, “L\infty -gain fuzzy control for nonlinear dynamic systems with persistent bounded disturbances,” in Proceedings of the IEEE International Conference on Fuzzy Systems, pp. 25-29, Budapest, Hungary, 2004.
[10] D. Liberzon and A. S. Morse, “Basic problems in stability and design of switched systems,” IEEE Control Systems Magazine, vol. 19, no. 5, pp. 59-70, 1999. · Zbl 1384.93064
[11] D. Liberzon, Switching in Systems and Control, Birkhäuser, Boston, Mass, USA, 2003. · Zbl 1036.93001
[12] X.-M. Sun, J. Zhao, and D. J. Hill, “Stability and L2-gain analysis for switched delay systems: a delay-dependent method,” Automatica, vol. 42, no. 10, pp. 1769-1774, 2006. · Zbl 1114.93086
[13] X. M. Sun, W. Wang, G. P. Liu, and J. Zhao, “Stability analysis for linear switched systems with time-varying delay,” IEEE Transactions on Systems, Man, and Cybernetics B, vol. 38, no. 2, pp. 528-533, 2008.
[14] T.-F. Li, J. Zhao, and G. M. Dimirovski, “Stability and L2-gain analysis for switched neutral systems with mixed time-varying delays,” Journal of the Franklin Institute, vol. 348, no. 9, pp. 2237-2256, 2011. · Zbl 1239.93103
[15] D. Y. Liu, S. M. Zhong, and Y. Q. Huang, “Stability and L2-gain analysis for switched neutral systems,” in Proceedings of the International Conference on Apperceiving Computing and Intelligence Analysis (ICACIA ’08), pp. 247-250, 2008.
[16] L. Xiong, S. Zhong, M. Ye, and S. Wu, “New stability and stabilization for switched neutral control systems,” Chaos, Solitons & Fractals, vol. 42, no. 3, pp. 1800-1811, 2009. · Zbl 1198.93187
[17] C. Li, T. Huang, G. Feng, and G. Chen, “Exponential stability of time-controlled switching systems with time delay,” Journal of the Franklin Institute, vol. 349, no. 1, pp. 216-233, 2012. · Zbl 1254.93136
[18] F. Gao, S. Zhong, and X. Gao, “Delay-dependent stability of a type of linear switching systems with discrete and distributed time delays,” Applied Mathematics and Computation, vol. 196, no. 1, pp. 24-39, 2008. · Zbl 1144.34050
[19] Z. R. Xiang and R. H. Wang, “Robust stabilization of switched non-linear systems with time-varying delays under asynchronous switching,” Proceedings of the Institution of Mechanical Engineers I, vol. 223, no. 8, pp. 1111-1128, 2009.
[20] L. Zhang and P. Shi, “Stability, L2-gain and asynchronous H\infty control of discrete-time switched systems with average dwell time,” IEEE Transactions on Automatic Control, vol. 54, no. 9, pp. 2192-2199, 2009. · Zbl 1367.93191
[21] W. Xiang, M. Che, C. Xiao, and Z. Xiang, “Stabilization of a class of switched systems with mismatched switching,” in Proceedings of the International Conference on Measuring Technology and Mechatronics Automation (ICMTMA ’09), pp. 124-127, Zhangjiajie, China, April 2009.
[22] L. Zhang and H. Gao, “Asynchronously switched control of switched linear systems with average dwell time,” Automatica, vol. 46, no. 5, pp. 953-958, 2010. · Zbl 1191.93068
[23] W. Xiang, J. Xiao, and M. N. Iqbal, “Robust observer design for nonlinear uncertain switched systems under asynchronous switching,” Nonlinear Analysis. Hybrid Systems, vol. 6, no. 1, pp. 754-773, 2012. · Zbl 1235.93053
[24] Z. Xiang, Y.-N. Sun, and Q. Chen, “Robust reliable stabilization of uncertain switched neutral systems with delayed switching,” Applied Mathematics and Computation, vol. 217, no. 23, pp. 9835-9844, 2011. · Zbl 1227.34075
[25] Z. R. Xiang and R. H. Wang, “Robust control for uncertain switched non-linear systems with time delay under asynchronous switching,” IET Control Theory & Applications, vol. 3, no. 8, pp. 1041-1050, 2009.
[26] D. Xie and X. Chen, “Observer-based switched control design for switched linear systems with time delay in detection of switching signal,” IET Control Theory & Applications, vol. 2, no. 5, pp. 437-445, 2008.
[27] Z. Ji, X. Guo, S. Xu, and L. Wang, “Stabilization of switched linear systems with time-varying delay in switching occurrence detection,” Circuits, Systems, and Signal Processing, vol. 26, no. 3, pp. 361-377, 2007. · Zbl 1118.93044
[28] Z. R. Xiang and R. H. Wang, “Robust control for uncertain switched non-linear systems with time delay under asynchronous switching,” IET Control Theory & Applications, vol. 3, no. 8, pp. 1041-1050, 2009.
[29] Z. G. Wu, P. Shi, H. Su, and J. Chu, “Delay-dependent stability analysis for switched neural networks with time-varying delay,” IEEE Transactions on Systems, Man, and Cybernetics B, vol. 41, no. 6, pp. 1522-1530, 2011.
[30] C. Yang and W. Zhu, “Stability analysis of impulsive switched systems with time delays,” Mathematical and Computer Modelling, vol. 50, no. 7-8, pp. 1188-1194, 2009. · Zbl 1185.34109
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.