H[infinity] Consensus of Multi-agent Systems with Random Time-Delay

This paper investigates the problem of H∞ synchronizations of multi-agent system with random time-delay. It is assumed that the topology of the system is fixed directed and connected. Considering that there are random communication time delays between the agents and additive perturbations, a consensus protocol is forwarded based on the consistence control algorithm. The delay is based on a given probability and the perturbations are assumed to be stable and bounded in H∞-norm by some priori given desired tolerance. By using Lyapunov analysis and stochastic techniques, the sufficient condition expressed in the form of LMI(Linear Matrix Inequality) is derived under which the system achieves its synchronization. All the agents finally synchronize to a dynamic reference state. Finally, a numerical example is presented to show the validity of the result.