Automated Synthesis of Lyapunov Functions for Multi-Agent Systems under Jointly Connected Topology

Abstract

This article investigates the consensus tracking problem of multi-agent systems under jointly connected topology through automated synthesis of Lyapunov functions. Based on the proposed distributed nonlinear control protocol, several consensus criteria for first-order multi-agent systems are established and certified by the construction and synthesis of more general polynomial Lyapunov functions. By employing sum-of-squares decomposition for multivariate polynomials, we can efficiently synthesize polynomial Lyapunov functions to achieve consensus verification in polynomial time, although the widely used quadratic Lyapunov functions do not exist. Moreover, polynomial coupling functions for our proposed protocol are concomitantly generated. Furthermore, the distributed nonlinear control protocol is extended to deal with second-order multi-agent systems, while ensuring second-order consensus verification. Finally, an example is presented to demonstrate the efficacy of our method.