Consensus in multi-agent with time-varying delays

The paper studies consensus problem in multi-agent with time-varying delays. By using orthogonal transformation techniques and variable substitution, the system is turned into two reduced dimensional system. Using theory of Lyapunov-Krasovskii function and techniques of integrator inequality, a sufficient condition expressed in LMI is given to guarantee all agents achieving consensus asymptotically for appropriate communication delays if the network topology is connected. Particularly, several feasible LMIs are proposed to determine the maximal allowable upper bound of time-varying delays. Simulation studies validate the effectiveness of the theoretical results.