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An invariance principle for nonlinear switched systems. (English) Zbl 1129.93443

Summary: We address the problem of extending LaSalle Invariance Principle to switched system. We prove an extension of the invariance principle relative to dwell time switched solutions, and a second one relative to constrained switched systems.

MSC:

93C57 Sampled-data control/observation systems
34A36 Discontinuous ordinary differential equations
34D20 Stability of solutions to ordinary differential equations
Full Text: DOI

References:

[1] Bacciotti, A., Stabilization by means of state space depending switching rules, Syst. Control Lett., 53, 195-201 (2004) · Zbl 1157.93480
[2] Bacciotti, A.; Ceragioli, F., Stability and stabilization of discontinuous systems and nonsmooth Liapunov functions, ESAIM COCV, 4, 361-437 (1999) · Zbl 0927.34034
[3] Branicky, M. S., Multiple Lyapunov functions and other analysis tools for switched and hybrid systems, IEEE Trans. Automat. Control, 43, 475-482 (1998) · Zbl 0904.93036
[4] Boscain, U., Stability of planar switched systems: the linear single input case, SIAM J. Control Optim., 41, 89-112 (2002) · Zbl 1012.93055
[5] 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
[6] DeCarlo, R. A.; Branicky, M. S.; Pettersson, S.; Lennartson, B., Perspectives and results on the stability and stabilization of hybrid system, Proc. IEEE, 88, 1069-1082 (2000)
[7] Filippov, A. F., Differential Equations with Discontinuous Righthand Sides (1988), Kluwer: Kluwer Dordrecht · Zbl 0664.34001
[8] Hespanha, J. P., Uniform stability of switched linear systems: extensions of LaSalle’s invariance principle, IEEE Trans. Automat. Control, 49, 4, 470-482 (2004) · Zbl 1365.93348
[9] Hespanha, J. P.; Liberzon, D.; Angeli, D.; Sontag, E. D., Nonlinear observability notions and stability of switched systems, IEEE Trans. Automat. Control, 50, 2, 154-168 (2005) · Zbl 1365.93349
[10] LaSalle, J. P.; Lefschetz, S., Stability by Liapunov’s Direct Method (1961), Academic Press: Academic Press London · Zbl 0098.06102
[11] Li, Z. G.; Wen, C. Y.; Soh, Y. C., Switched controllers and their applications in bilinear systems, Automatica, 37, 447-481 (2001) · Zbl 0978.93060
[12] Liberzon, D., Switching in Systems and Control (2003), Birkhäuser: Birkhäuser Boston · Zbl 1036.93001
[13] 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
[14] Lygeros, J.; Simic, S. N.; Johansson, K. H.; Zhang, J.; Sastry, S. S., Dynamical properties of hybrid automata, IEEE Trans. Automat. Control, 48, 2-17 (2003) · Zbl 1364.93503
[15] Mancilla-Aguilar, J. L.; Garcia, R. A., A converse Lyapunov theorem for nonlinear switched systems, Syst. Control Lett., 41, 67-71 (2000) · Zbl 1054.93515
[16] Shevitz, D.; Paden, B., Lyapunov stability theory of nonsmooth systems, IEEE Trans. Automat. Control, 39, 1910-1914 (1994) · Zbl 0814.93049
[17] Zhang, J.; Johansson, K. H.; Lygeros, J.; Sastry, S. S., Dynamical systems revisited: hybrid systems with Zeno executions, (Lynch, N.; Krogh, B. H., Proceedings of the Third International Workshop on Hybrid Systems: Computation and Control, Lectures Notes in Computer Science, vol. 1790 (2000), Springer: Springer Berlin), 451-464 · Zbl 0982.93046
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