A Universal Stability Criterion for Nonlinear Interconnected Systems with Generalized Supply Rates

Abstract

In this paper, a new approach to stability and performance of nonlinear interconnected systems is developed by smoothly generalizing a recently-introduced method of the state-dependent scaling. A set of popular Lyapunov stability criteria, the Input-to-State Stability(ISS) small-gain theorem and the scaled H^∞ small-gain condition (or structured singular value) are included as special cases. The criteria show us how to construct Lyapunov functions explicitly.