Estimate of the domain of attraction for interconnected systems

Abstract

In this paper, we estimate the domain of attraction of the origin of two interconnected nonlinear systems. For each subsystem we introduce an auxiliary system and assume that the origin is locally robustly asymptotically stable. Then an integral input-to state stable Lyapunov function for each subsystem on a bounded set is constructed via Zubov’s method and the introduced auxiliary system. A local version of small gain theorem is proposed. It is easier to check if the conditions of the proposed small gain theorem are satisfied. Moreover, an estimate for the domain of attraction for the whole system is obtained based on the proposed small gain theorem and the computed integral input-to state stable Lyapunov functions. We illustrate the effectiveness of the main results by an academic example.