Exponential synchronization of nonlinear multi-agent systems with time delays and impulsive disturbances

Summary The problem of cooperative synchronization of nonlinear multi-agent systems with time delays is investigated in this paper. Compared with the existing works about synchronization (or consensus) of multi-agent systems, the method in this paper provides a more general framework by considering nonlinear multi-agent systems with time delays and impulsive disturbances. The model in this paper is sufficiently general to include a class of delayed chaotic systems. Based on the Lyapunov stability theory and algebraic graph theory, sufficient conditions are presented to guarantee the cooperative exponential synchronization for these multi-agent delayed nonlinear systems. These conditions are expressed in terms of linear matrix inequalities, which can easily be checked by existing software tools. It is seen that the Lyapunov functions must be constructed based on the graph topology to prove synchronization. The well-known master-slave (drive-response) synchronization of two chaotic delayed systems is a special case of this paper, and therefore, the results in this paper are also useful for practical applications in secure communication. Simulation results verify the effectiveness of the proposed synchronization control algorithm.