Safety Verification of Nonlinear Switched Systems via Barrier Functions and Barrier Densities

This paper extends some existing methods of safety verification of nonlinear systems to the case of nonlinear switched systems with time-dependent switching. Barrier functions and barrier densities are applied to safety verification of nonlinear switched systems. In particular, sufficient conditions for safety of switched systems are given based on the existence of a common Barrier function or a common Barrier density. Theoretical results are exemplified applying a sum of squares method with the Putinar positivstellensatz to find barrier functions and barrier densities certifying safety.