Nonpathological ISS-Lyapunov Functions for Interconnected Differential Inclusions

This article concerns robustness analysis for interconnections of two dynamical systems (described by upper semicontinuous differential inclusions) using a generalized notion derivatives associated with locally Lipschitz Lyapunov functions obtained from finite family differentiable functions. We first provide sufficient conditions input-to-state stability inclusions, class nonsmooth (but Lipschitz) candidate and the concept Lie derivative. In general our are less conservative than more common Clarke derivative-based conditions. apply result to state-dependent switched systems, interconnection inclusions. As an example, we propose observer-based controller certain nonlinear two-mode systems.