Relaxing Global Decrescence Conditions in Lyapunov Theorems for Hybrid Systems
نویسندگان
چکیده
Lyapunov methods have been successfully applied to compute the Region of Attraction (ROA) of a system, i.e. the set of states that remain invariant for all time. A popular method for constructing Lyapunov functions is the Sum of Squares (SOS) approach. Current methods for determining stability of hybrid systems using SOS require either stability over the entire hybrid guard or knowledge of the switching times, limiting the types of systems that can be analyzed. In this paper, we introduce a new method to relax these constraints by only requiring decrescence properties over the ‘active’ subsections of each guard. We introduce our new formulation, explore useful modeling techniques, then apply them to five examples.
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تاریخ انتشار 2014