Robust Stability Analysis of Nonlinear Switched Systems with Filippov Solutions

This paper addresses the stability problem of a class of nonlinear switched systems with partitioned state-space and state-dependent switching. In lieu of the Carathéodory solutions, the general Filippov solutions are considered. This encapsulates solutions with infinite switching in finite time. Based on the theory of differential inclusions, a Lyapunov stability theorem is brought forward. These results are also extended to switched systems subject to polytopic uncertainty. Furthermore, the proposed stability theorems are reformulated using the sum of squares decomposition method which provides sufficient means to construct the corresponding Lyapunov functions via available semi-definite programming techniques.