×

A stability condition with delay-dependence for a class of switched large-scale time-delay systems. (English) Zbl 1266.93130

Summary: By using the time-switched method and the comparison theorem, we derived a criterion of delay-dependent stability for the switched large-scale time-delay systems. To guarantee the exponential stability for the switched large-scale time-delay systems with stability margin \(\lambda\), the total activation time ratio of the switching law is determined. An example is used to illustrate the effectiveness of our result.

MSC:

93D20 Asymptotic stability in control theory
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] 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 · doi:10.1109/37.793443
[2] Z. Ji, L. Wang, G. Xie, and F. Hao, “Linear matrix inequality approach to quadratic stabilisation of switched systems,” IEE Proceedings: Control Theory and Applications, vol. 151, no. 3, pp. 289-294, 2004. · doi:10.1049/ip-cta:20040306
[3] J. S. Chiou and C. M. Cheng, “Stabilization analysis of the switched discrete-time systems using Lyapunov stability theorem and genetic algorithm,” Chaos, Solitons and Fractals, vol. 42, no. 2, pp. 751-759, 2009. · Zbl 1198.93175 · doi:10.1016/j.chaos.2009.02.003
[4] J. S. Chiou and C. J. Wang, “Stability analysis and time-switching rule design for the switched continuous-time and discrete-time systems,” International Journal of Nonlinear Sciences and Numerical Simulation, vol. 11, pp. 115-118, 2010. · Zbl 1401.93174
[5] J. P. Hespanha and A. S. Morse, “Stability of switched systems with average dwell-time,” in Proceedings of the 38th IEEE Conference on Decision and Control (CDC), pp. 2655-2660, Phoenix, Ariz, USA, December 1999.
[6] G. Zhai, B. Hu, K. Yasuda, and A. N. Michel, “Stability analysis of switched systems with stable and unstable subsystems: an average dwell time approach,” International Journal of Systems Science, vol. 32, no. 8, pp. 1055-1061, 2001. · Zbl 1022.93043 · doi:10.1080/00207720010015690
[7] S. H. Lee, T. H. Kim, and J. T. Lim, “New stability analysis of switched systems,” Automatica, vol. 36, no. 6, pp. 917-922, 2000. · Zbl 0953.93015 · doi:10.1016/S0005-1098(99)00208-3
[8] C. D. Persis, R. D. Santis, and A. S. Morse, “Switched nonlinear systems with state-dependent dwell-time,” Systems and Control Letters, vol. 50, no. 4, pp. 291-302, 2003. · Zbl 1157.93510 · doi:10.1016/S0167-6911(03)00161-0
[9] J. S. Chiou, C. J. Wang, and C. M. Cheng, “On delay-dependent stabilization analysis for the switched time-delay systems with the state-driven switching strategy,” Journal of the Franklin Institute, vol. 348, no. 2, pp. 261-276, 2011. · Zbl 1218.34091 · doi:10.1016/j.jfranklin.2010.11.006
[10] C. J. Wang, J. S. Chiou, and C. M. Cheng, “On delay-independent stabilization analysis for a class of switched time-delay systems with the state-driven switching strategy,” Journal of the Franklin Institute, vol. 348, no. 9, pp. 2292-2307, 2011. · Zbl 1239.93080 · doi:10.1016/j.jfranklin.2011.06.018
[11] X. Xiao and Z. Mao, “Decentralized guaranteed cost stabilization of time-delay large-scale systems based on reduced-order observers,” Journal of the Franklin Institute, vol. 348, no. 9, pp. 2689-2700, 2011. · Zbl 1239.93109 · doi:10.1016/j.jfranklin.2011.08.012
[12] J. S. Chiou, “Stability analysis for a class of switched large-scale time-delay systems via time-switched method,” IEE Proceedings: Control Theory and Applications, vol. 153, no. 6, pp. 684-688, 2006. · doi:10.1049/ip-cta:20050292
[13] P. Lancaster, Theory of Matrices, Academic Press, New York, NY, USA, 1969. · Zbl 0186.05301
[14] V. B. Kolmanovskii and V. R. Nosov, Stability of Functional Differential Equations, vol. 180 of Mathematics in Science and Engineering, Academic Press, London, UK, 1986. · Zbl 0593.34070
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.