Containment control of linear discrete-time fractional-order multi-agent systems with time-delays

Abstract

This work concerns with containment control of discrete-time fractional-order multi-agent systems with time-delay. A directed fixed topology is considered for the agents. At first, necessary and sufficient conditions to ensure the asymptotic stability of a general linear discrete-time fractional-order system with input time-delay are extracted. Then, a multi-agent system that the dynamics of its agents are represented with discrete-time fractional-order integrators with input time-delay is considered. Now, the obtained stability conditions are employed to derive the required conditions in terms of the control gains to realize the containment control of the mentioned multi-agent system. Numerical simulations demonstrate that the positions of the followers tend to the convex hull constructed by the leaders.