Leader-Following Group Consensus of Discrete-Time Fractional-Order Multi-Agent Systems with Time-Delay

In this paper, the leader-following group consensus of discrete-time fractional-order multi-agent systems with time-delay is studied. At First, two groups are considered. Then, the problem is extended to arbitrary number of groups. The agents are considered as discrete-time fractional order integrators with input time delay . The interaction between agents is described with a directed communication graph with fixed topology. The group consensus problem for the considered agents leads to asymptotic stability analysis of a discrete-time fractional order system with time-delay. Based on this idea, the necessary and sufficient condition to reach the leader-following group consensus in terms of the controller gains of agents is extracted. Moreover, the optimal value of the controller gains is calculated to minimize a special performance index. Numerical simulations show the performance of the proposed method.