Consensus Criterion Verification for Heterogeneous Multiagent Systems via Sum-of-Squares Programming

This article is concerned with consensus for heterogeneous multi-agent systems under distributed nonlinear control protocol. Based on general Lyapunov functions beyond the quadratic form, a less conservative consensus criterion is proposed in the presence of only a directed spanning tree. Then, the consensus problem for polynomial systems can be converted into a sum-of-squares programming problem, yielding polynomial Lyapunov functions efficiently to realize the consensus criterion verification. The benefits of our method are twofold. One is the automatic verification of consensus for the heterogeneous multi-agent systems, for which the widely used quadratic Lyapunov functions may not exist. The other one is the flexible generalization ability to deal with certain nonpolynomial multi-agent systems. Finally, the theoretical and algorithmic developments are demonstrated on three numerical examples.