Lyapunov Functions for General Networks of iISS Systems via Small-Gain Criteria: A Dissipative Formulation

摘要

This paper considers dynamical networks consisting of integral input-to-state stable (iISS) subsystems interconnected in a general way. The purpose is to give a solution to the problem of verifying stability of the networks for the first time. The iISS small-gain theorem developed recently has been restricted to interconnection of two subsystems. Recent nonlinear small-gain results on stability of large-scale systems have been obtained only for input-to-state stable stable (ISS) subsystems. Allowing non-ISS subsystems in the networks invalidates their key techniques. This paper shows how to construct Lyapunov functions of such networks by means of nonlinear sum of individual Lyapunov functions of subsystems.