Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
1713879 | Nonlinear Analysis: Hybrid Systems | 2008 | 9 Pages |
Abstract
In [H. Ye, A.N. Michel, L. Hou, Stability theory for hybrid dynamical systems, IEEE Transactions on Automatic Control 43 (4) (1998) 461–474] we established, among other results, a set of sufficient conditions for the uniform asymptotic stability of invariant sets for discontinuous dynamical systems (DDS) defined on metric space, and under some additional minor assumptions, we also established a set of necessary conditions (a converse theorem). This converse theorem involves Lyapunov functions which need not necessarily be continuous. In the present paper, we show that under some additional very mild assumptions, the Lyapunov functions for the converse theorem need actually be continuous.
Related Topics
Physical Sciences and Engineering
Engineering
Control and Systems Engineering
Authors
Ling Hou, Anthony N. Michel,