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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. © 2011 IEEE.
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