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Zhai, Guisheng; Hu, Bo; Yasuda, Kazunori; Michel, Anthony N.

Disturbance attenuation properties of time-controlled switched systems. (English) Zbl 1022.93017

J. Franklin Inst. 338, No. 7, 765-779 (2001).
The authors study disturbance attenuation properties for time-controlled switched systems by using an average dwell time approach incorporated with a piecewise Lyapunov function. The authors have extended the results to the case where not all subsystems are Hurwitz stable. The authors have also discussed the case in which nonlinear norm-bounded perturbations exist in the subsystems.
Reviewer: Seenith Sivasundaram (Daytona Beach)

Cited in 181 Documents

MSC:

93B51 Design techniques (robust design, computer-aided design, etc.)
93C30 Control/observation systems governed by functional relations other than differential equations (such as hybrid and switching systems)
93C73 Perturbations in control/observation systems
93B12 Variable structure systems

Keywords:

disturbance attenuation; time controlled switched systems; Lyapunov function; perturbation

Software:

LMI toolbox; Matlab; Control System Toolbox
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\textit{G. Zhai} et al., J. Franklin Inst. 338, No. 7, 765--779 (2001; Zbl 1022.93017)
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References:

[1] Liberzon, D.; Morse, A.S., Basic problems in stability and design of switched systems, IEEE control systems magazine, 19, 15, 59-70, (1999) · Zbl 1384.93064
[2] Dayawansa, W.P.; Martin, C.F., A converse Lyapunov theorem for a class of dynamical systems which undergo switching, IEEE trans. automat. control, 44, 4, 751-760, (1999) · Zbl 0960.93046
[3] Wicks, M.A.; Peleties, P.; DeCarlo, R.A., Switched controller synthesis for the quadratic stabilization of a pair of unstable linear systems, Eur. J. control, 4, 140-147, (1998) · Zbl 0910.93062
[4] Morse, A.S., Supervisory control of families of linear set-point controllers—part 1: exact matching, IEEE trans. automat. control, 41, 10, 1413-1431, (1996) · Zbl 0872.93009
[5] B. Hu, G. Zhai, A.N. Michel, Hybrid output feedback stabilization of two-dimensional linear control systems, Proceedings of the 2000 American Control Conference, 2000, pp. 2184-2188.
[6] Hu, B.; Michel, A.N., Stability analysis of digital feedback control systems with time-varying sampling periods, Automatica, 36, 897-905, (2000) · Zbl 0941.93034
[7] J.P. Hespanha, A.S. Morse, Stability of switched systems with average dwell-time, Proceedings of the 38th IEEE Conference on Decision and Control, 1999, pp. 2655-2660.
[8] G. Zhai, B. Hu, K. Yasuda, A.N. Michel, Stability analysis of switched systems with stable and unstable subsystems: an average dwell time approach, Proceedings of the 2000 American Control Conference, 2000, pp. 200-204. · Zbl 1022.93043
[9] Branicky, M.S., Multiple Lyapunov functions and other analysis tools for switched and hydrid systems, IEEE trans. automat. control, 43, 4, 475-482, (1998) · Zbl 0904.93036
[10] Ye, H.; Michel, A.N.; Hou, L., Stability theory for hybrid dynamical systems, IEEE trans. automat. control, 43, 4, 461-474, (1998) · Zbl 0905.93024
[11] S. Pettersson, B. Lennartson, LMI for stability and robustness of hybrid systems, Proceedings of the 1997 American Control Conference, 1997, pp. 1714-1718.
[12] M.A. Wicks, P. Peleties, R.A. DeCarlo, Construction of piecewise Lyapunov functions for stabilizing switched systems, Proceedings of the 33rd IEEE Conference on Decision and Control, 1994, pp. 3492-3497.
[13] B. Hu, X. Xu, A.N. Michel, P.J. Antsaklis, Stability analysis for a class of nonlinear switched systems, Proceedings of the 38th IEEE Conference on Decision and Control, 1999, pp. 4374-4379.
[14] J.P. Hespanha, Logic-based switching algorithms in control, Ph.D. Dissertation, Yale University, 1998.
[15] G. Zhai, B. Hu, K. Yasuda, A.N. Michel, Piecewise Lyapunov functions for switched systems with average dwell time, Proceedings of the 2000 Asian Control Conference, 2000, pp. 229-233.
[16] Gahinet, P.; Apkarian, P., A linear matrix inequality approach to H∞ control, Int. J. robust nonlinear control, 4, 421-448, (1994) · Zbl 0808.93024
[17] Boyd, S.; El Ghaoui, L.; Feron, E.; Balakrishnan, V., Linear matrix inequalities in system and control theory, (1994), SIAM Philadelphia, PA · Zbl 0816.93004
[18] G. Gahinet, A. Nemirovski, A.J. Laub, M. Chilali, LMI Control Toolbox for Use with Matlab, the MathWorks Inc., 1995.
[19] Miller, R.K.; Michel, A.N., Ordinary differential equations, (1982), Academic Press New York · Zbl 0499.34024
[20] Narendra, K.S.; Balakrishnan, J., A common Lyapunov function for stable LTI systems with commuting A-matrices, IEEE trans. automat. control, 39, 12, 2469-2471, (1994) · Zbl 0825.93668
[21] van der Schaft, A.J., L2-gain analysis of nonlinear systems and nonlinear state feedback H∞ control, IEEE trans. automat. control, 37, 6, 770-784, (1992) · Zbl 0755.93037
[22] Khalil, H.K., Nonlinear systems, (1996), Prentice-Hall Englewood Cliffs, NJ · Zbl 0626.34052
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.