A Nested {M}atrosov Theorem for Hybrid Systems
Submitted by ricardo on February 28, 2017 - 2:36pm
Title | A Nested {M}atrosov Theorem for Hybrid Systems |
Publication Type | Conference Paper |
Year of Publication | 2008 |
Authors | Sanfelice R.G, Teel A.R |
Conference Name | Proc. 27th American Control Conference |
Keywords | hybrid systems |
Abstract | 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. |
URL | https://hybrid.soe.ucsc.edu/files/preprints/27.pdf |
DOI |