A new small gain theorem for large-scale networks of switched systems with arbitrary switchings

We consider a large-scale switched nonlinear system which is composed as an interconnection of N nonlinear switched systems. Having assumed that every subsystem is ISpS (ISS) uniformly with respect to the unobservable switching signals, we prove a small-gain condition for the overall large-scale system to be ISpS (respectively ISS) uniformly with respect to the unknown switching signal. To solve the problem we extend the well-known result by E.D. Sontag and Y. Wang on characterizations of input-to-state stability property to the case of uniform ISS of switched systems with arbitrary switchings.

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