State-dependent scaling characterization of stability and performance for nonlinear interconnected systems

This paper proposes new criteria for stability and performance of nonlinear interconnected systems by smoothly generalizing a recently-developed method of the state-dependent scaling. The criteria are directly related to Lyapunov functions so that they show how to construct Lyapunov functions which establish the desired stability and performance explicitly. A set of popular Lyapunov stability criteria, the input-to-state stability, small-gain theorem and scaled H;^∞ small-gain condition (or structured singular value) are included as special cases. The results are obtained by introducing state-dependent scaling into a Lyapunov stability approach to dissipative systems.