Estimating the Region of Attraction for Switched Nonlinear Systems: A Continuous Piecewise Lyapunov Function Approach

Computing the Region of Attraction (RA) of switched nonlinear systems is an interesting but challenging problem. Approaches based on a common Lyapunov function are effective, while the estimation result is sometimes conservative when switched systems do not share a common Lyapunov function. For estimating the RA of switched polynomial systems, this paper proposes a method via a piecewise polynomial Lyapunov function. The main idea is to find a Lyapunov function separately for each subsystem, and to guarantee the continuity of Lyapunov functions in the transitions amongst subsystems. The sublevel sets of piecewise Lyapunov functions are exploited to inner-approximate the RA, and less conservative results are obtained compared to the common Lyapunov function approach. Finally, the effectiveness of proposed method is illustrated by examples.