Stability Verification for Heterogeneous Complex Networks via Iterative SOS Programming

This letter is to investigate the stability verification for heterogeneous polynomial complex networks through iterative sum-of-squares programming approach. With polynomial Lyapunov functions, a global asymptotic stability criterion is established for the heterogeneous complex networks under the directed topology. Based on the proposed criterion, the stability verification problem is then reduced to a sum-of-squares optimization problem for solving polynomial matrix inequalities. To process non-convex terms of the polynomial matrix inequalities, we present an iterative sum-of-squares programming approach to turn them into the convex polynomial matrix inequalities, yielding polynomial Lyapunov functions effectively to realize the stability verification. Finally, a numerical example is given to show the fully automatic verification of global asymptotic stability for the heterogeneous polynomial complex networks, which demonstrates the theoretical and algorithmic advantages of the proposed method.

I. Introduction

The collaborative research of multi-agent networked systems has gained increasing prominence in both military and civilian domains due to its broad applications: formation flying of multiple satellites [1], multi-robot systems [2], wireless sensor networks [3], and so forth. One of the fundamental issues for the collaboration of complex networked systems is to design a distributed control protocol such that all agents realize the common collective behaviors, e.g., stability [4], [5], [6], and consensus [7], [8], [9].