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General Lyapunov Functions for Consensus of Nonlinear Multiagent Systems

In this brief, we investigate the consensus problem of nonlinear multiagent systems by means of general Lyapunov functions. That is, by constructing general Lyapunov functions, such as polynomial Lyapunov functions beyond quadratic forms, a sufficient condition is established for achieving global consensus. Compared with the existing consensus criteria deduced by quadratic Lyapunov functions, our consensus criterion is less conservative and can be applicable for more systems. In particular, for polynomial systems and even certain classes of nonpolynomial systems, our consensus criterion can be formulated based on polynomial Lyapunov functions, which can be calculated by using the sum-of-squares (SOS) programming tools such as SOSTOOLS. Finally, two simulation examples are given to illustrate the effectiveness of our proposed theoretical results.