  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.
