×

Stabilization analysis of the switched discrete-time systems using Lyapunov stability theorem and genetic algorithm. (English) Zbl 1198.93175

Summary: This paper attempts to investigate the stabilization and switching law design for the switched discrete-time systems. A theoretical study of the stabilization and switching law design has been performed using the Lyapunov stability theorem and genetic algorithm. The present results demonstrated that can be applied to cases when all individual subsystems are unstable. Finally, some examples are exploited to illustrate the proposed schemes.
Editorial remark: There are doubts about a proper peer-reviewing procedure of this journal. The editor-in-chief has retired, but, according to a statement of the publisher, articles accepted under his guidance are published without additional control.

MSC:

93D15 Stabilization of systems by feedback
39A30 Stability theory for difference equations
93C55 Discrete-time control/observation systems
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Liberzon, D.; Morse, A. S., Basic problems in stability and design of switched systems, IEEE Control Syst Mag, 19, 59-70 (1999) · Zbl 1384.93064
[2] Hofbaur, M. W.; Williams, B. C., Hybrid estimation of complex systems, IEEE Trans Syst Man Cybernet B Cybernet, 34, 2178-2191 (2004)
[3] EI Naschie, M. S., Super strings, entropy and the elementary particles content of the standard model, Chaos, Solitons & Fractals, 29, 1, 48-54 (2006) · Zbl 1098.81816
[4] EI Naschie, M. S., Fractal black holes and information, Chaos, Solitons & Fractals, 29, 1, 23-35 (2006) · Zbl 1131.85301
[5] EI Naschie, M. S., Holographic correspondence and quantum gravity in \(E\)-infinity spacetime, Chaos, Solitons & Fractals, 29, 1, 871-875 (2006)
[6] Cervantes, I.; Femat, R.; Leyva-Ramos, J., Study of a class of hybrid-time systems, Chaos, Solitons & Fractals, 32, 1081-1095 (2007) · Zbl 1133.34304
[7] Agrachev, A. A.; Liberzon, D., Lie-algebraic stability criteria for switched systems, SIAM J Control Opt, 41, 253-269 (2001) · Zbl 0995.93064
[8] Cheng, D.; Guo, L.; Huan, J., On quadratic Lyapunov functions, IEEE Trans Automat Control, 48, 885-890 (2003) · Zbl 1364.93557
[9] Dayawansa, W. P.; Martin, C. F., A converse Lyapunov theorem for a class of dynamical systems which undergo switching, IEEE Trans Automat Control, 44, 751-760 (1999) · Zbl 0960.93046
[10] Li, Z. G.; Wen, C. Y.; Soh, Y. C., Stabilization of a class of switched systems via designing switching laws, IEEE Trans Automat Control, 46, 665-670 (2001) · Zbl 1001.93065
[11] Sun, Z.; Ge, S. S., Analysis and synthesis of switched linear control systems, Automatica, 41, 181-195 (2005) · Zbl 1074.93025
[12] Skafidas, E.; Evans, R. J.; Savkin, A. V.; Petersen, I. R., Stability results for switched controller systems, Automatica, 35, 553-556 (1999) · Zbl 0949.93014
[13] Hespanha JP, Morse AS. Stability of switched systems with average dwell-time. In: Proceedings of the IEEE Conference Decision and Control; 1999. p. 2655-60.; Hespanha JP, Morse AS. Stability of switched systems with average dwell-time. In: Proceedings of the IEEE Conference Decision and Control; 1999. p. 2655-60.
[14] Zhai, G.; Hu, B.; Yasuda, K.; Michel, A. N., Stability analysis of switched systems with stable and unstable subsystems: an average dwell time approach, Int J Syst Sci, 32, 1055-1061 (2001) · Zbl 1022.93043
[15] Lu, B.; Wu, F., Switching LPV control design using multiple parameter-dependent Lyapunov functions, Automatica, 40, 1973-1980 (2004) · Zbl 1133.93370
[16] Lee, S. H.; Kim, T. H.; Lim, J. T., A new stability analysis of switched systems, Automatica, 36, 917-922 (2000) · Zbl 0953.93015
[17] Chiou, J.-S., Stability analysis for a class of switched large-scale time-delay systems via time-switched method, IEE Proc Control Theory Appl, 153, 684-688 (2006)
[18] Ji Z, Wang L. Quadratic stabilization of uncertain discrete-time switched linear system. In: Proceedings of the IEEE Conference on Systems, Man and Cybernetics; 2004. p. 1492-7.; Ji Z, Wang L. Quadratic stabilization of uncertain discrete-time switched linear system. In: Proceedings of the IEEE Conference on Systems, Man and Cybernetics; 2004. p. 1492-7.
[19] Xie G, Wang L. Stabilization of a class of hybrid discrete-time systems. In: Proceedings of the IEEE Conference on Control Applications; 2003. p. 1404-9.; Xie G, Wang L. Stabilization of a class of hybrid discrete-time systems. In: Proceedings of the IEEE Conference on Control Applications; 2003. p. 1404-9.
[20] Zhai G, Lin H, Michel AN, Yasuda K. Stability analysis for switched systems with continuous-time and discrete-time subsystems. In: Proceedings of the American Control Conference; 2004. p. 4555-60.; Zhai G, Lin H, Michel AN, Yasuda K. Stability analysis for switched systems with continuous-time and discrete-time subsystems. In: Proceedings of the American Control Conference; 2004. p. 4555-60.
[21] Daafouz, J.; Riedinger, P.; Iung, C., Stability analysis and control synthesis for switched systems: a switched Lyapunov function approach, IEEE Trans Automat Control, 47, 1883-1887 (1999) · Zbl 1364.93559
[22] Xie, D.; Wang, L.; Hao, F.; Xie, G., LMI approach to \(\text{L}_2\) gain analysis and control synthesis of uncertain switched systems, IEE Proc Control Theory Appl, 151, 21-28 (2004)
[23] Xie D, Wang L, Hao F, Xie G. Robust stability analysis and control synthesis for discrete-time uncertain switched systems. In: Proceedings of the IEEE Conference Decision and Control; 2003. p. 4812-7.; Xie D, Wang L, Hao F, Xie G. Robust stability analysis and control synthesis for discrete-time uncertain switched systems. In: Proceedings of the IEEE Conference Decision and Control; 2003. p. 4812-7.
[24] Sun, Z., Sampling and control of switched linear systems, J Franklin Inst, 341, 657-674 (2004) · Zbl 1064.94566
[25] Sheng, W.; Swift, S.; Zhang, L.; Liu, X., A weight sum validity function for clustering with a hybrid niching genetic algorithm, IEEE Trans Syst Man Cybernet B Cybernet, 35, 1156-1167 (2005)
[26] Wu, M. S.; Teng, W. C.; Jeng, J. H.; Hsieh, J. G., Spatial correlation genetic algorithm for fractal image compression, Chaos, Solitons & Fractals, 28, 497-510 (2006) · Zbl 1084.68941
[27] Wu, Y. T.; Shih, F. Y., Genetic algorithm based methodology for breaking the steganalytic systems, IEEE Trans Syst Man Cybernet B Cybernet, 36, 24-31 (2006)
[28] Guo, J.; Xie, G.; Wang, L., Chaotic attractor generation and critical value analysis via switching approach, Chaos, Solitons & Fractals, 40, 2160-2169 (2009) · Zbl 1198.37046
[29] Letellier, C.; Bennoud, M.; Martel, G., Intermittency and period-doubling cascade on tori in a bimode laser model, Chaos, Solitons & Fractals, 33, 782-794 (2007)
[30] Cervantes, I.; Femat, R.; Leyva-Ramos, J., Study of a class of hybrid-time systems, Chaos, Solitons & Fractals, 32, 1081-1095 (2007) · Zbl 1133.34304
[31] Horbelt, W.; Timmer, J.; Bunner, M. J.; Meucci, R.; Ciofini, M., Dynamical modeling of measured time series from a Q-switched \(CO_2\) laser, Chaos, Solitons & Fractals, 17, 397-404 (2003) · Zbl 1033.37040
[32] Li, P.; Zhong, S. M.; Cui, J. Z., Stability analysis of linear switching systems with time delays, Chaos, Solitons & Fractals, 40, 474-480 (2009) · Zbl 1197.34138
[33] Chiou, J. S.; Cheng, C. M., Stabilization analysis for a class of switched discrete-time systems, IEEE Conf Syst Man Cybernet, 6, 4535-4540 (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.