Existence of Common Lyapunov Function based on KKM lemma for switched Persidskii-type systems

The paper addresses the existence problem of the Common Lyapunov Function (CLF for short) for several classes of switched nonlinear systems, where each subsystem has the structure of Persidskii-type system. Some sufficient conditions are given via the variant of the well-known Knaster - Kuratowski - Mazurkiewicz (KKM for short) lemma, which guarantees the existence of the CLF of switched nonlinear systems, and moreover the constructive method for a CLF of the switched nonlinear system is presented.