On Robust Stability of Switched Systems in the Context of Filippov Solutions

The stability problem of a class of nonlinear switched systems defined on compact sets with state-dependent switching is considered. Instead of the Caratheodory solutions, the general Filippov solutions are studied. This encapsulates solutions with infinite switching in finite time and sliding modes in the neighborhood of the switching surfaces. In this regard, a Lyapunov-like stability theorem, based on the theory of differential inclusions, is formulated. Additionally, the results are extended to switched systems with simplical uncertainty. It is also demonstrated that, for the special case of polynomial switched systems defined on semi-algebraic sets, stability analysis can be checked based on sum of squares programming techniques.