Consensus of switched multi-agents system with cooperative and competitive relationship

In this paper, the consensus problem of a class of linear multi-agent systems is analysed. In our model, switching between subnetworks and competition between agents is considered simultaneously. We suppose that all subnetworks cannot achieve a consensus and switching signal has a minimum dwell time. By using the time-dependent quadratic Lyapunov function and the average dwell time method, a consensus condition of switched networks is obtained. By using the sum of squares (SOS) programming in the software package SOSTOOLS of Matlab, these resulting conditions can be implemented. The results obtained are also extended to uncertain linear multi-agent systems. Finally, a simulation example is given to illustrate the validity of our results.