Leader-following exponential consensus control for discrete-time multi-agent systems with time-varying communication delay and unmeasured state: two general methods

This paper studies the leader-following exponential consensus of discrete-time multi-agent systems with time-varying communication delay by means of the relative-output-based and observer-based methods. In the presence of time-varying communication delay, the relative-output-based and observer-based protocols are provided respectively. Relying on the model transformation method, the exponential consensus problem is reformulated into the stability problem of the augmented time-delay error systems by means of an exponent transformation technique. Based on the delay-based multiple Lyapunov function, a sufficient condition to ensure the exponential consensus is formulated into linear matrix inequality by means of a structure separation technique. Simulation studies are utilized to validate the proposed method.