@conference {27,
	title = {A Nested {M}atrosov Theorem for Hybrid Systems},
	booktitle = {Proc. 27th American Control Conference},
	series = {NULL},
	year = {2008},
	pages = {2915{\textendash}2920},
	abstract = {We present a sufficient condition for uniform global asymptotic stability of compact sets for hybrid systems. Uniform global asymptotic stability (UGAS {\textendash} 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{\textquoteright}s theorem are a reasonable alternative to LaSalle{\textquoteright}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.},
	keywords = {hybrid systems},
	doi = {http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=\&arnumber=4586938\&isnumber=4586444:PDF;SLIDES:Talks/ACC2008-ThB14-5.pdf:PowerPoint},
	url = {https://hybrid.soe.ucsc.edu/files/preprints/27.pdf},
	author = {R. G. Sanfelice and A. R. Teel}
}
