Consensus Analysis for Linear Multi-agent Systems with Time-varying Delays

This paper concerns the consensus problem for linear multi-agent systems with time-varying delays. A consensus protocol is built upon the relative output information between neighboring agents in the presence of time-varying delays. Some delay-dependent conditions are derived based on linear matrix inequalities to achieve consensus. In the case that the feedback gain matrix K is known, the Lyapunov functional theory together with the convex combination technique are used. In the case that K is unknown, the variable substitute approach is introduced to convert nonlinear matrix inequalities into linear matrix inequalities, which are easily verified via GEVP solver in Matlab Toolbox to guarantee consensus for linear multi-agent systems. Finally, two numerical examples and simulation results are presented which demonstrate the effectiveness of the proposed results.