A Nested Matrosov Theorem for Hybrid Systems

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E. Conference Papers


Proc. 27th American Control Conference, Issue NULL, p.2915–2920 (2008)

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hybrid systems


We present a sufficient condition for uniform global asymptotic stability of compact sets for hybrid systems. Uniform global asymptotic stability (UGAS – in the sense that bounds on the solutions and on the convergence time depend only on the distance to the compact set of interest) are introduced for a large class of hybrid systems which are given by a flow map, flow set, jump map, and jump set. We show that uniform global stability of a compact set plus the existence of Lyapunov-like functions and continuous functions satisfying a nested condition on the flow and jump sets imply uniform global asymptotic stability of the compact set. The required nested condition for hybrid systems turns out to be a combination of the conditions in nested Matrosov theorems for time-varying continuous-time and discrete-time available in the literature. Our result also show that Matrosov's theorem are a reasonable alternative to LaSalle's invariance principle for time-invariant systems when additional functions with certain decreasing properties are available. We illustrate the application of our main result in several examples, including the so-called bouncing ball system.


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