Relative controllability of multiagent systems with pairwise different delays in states

In this manuscript, relative controllability of leader–follower multiagent systems with pairwise different delays in states and fixed interaction topology is considered. The interaction topology of the group of agents is modeled by a directed graph. The agents with unidirectional information flows are selected as leaders, and the others are followers. Dynamics of each follower obeys a generic time-invariant delay differential equation, and the delays of agents, which satisfy a specified condition, are different one another because of the degeneration or burn-in of sensors. With a neighbor-based protocol steering, the dynamics of followers become a compact form with multiple delays. Solution of the multidelayed system without pairwise matrices permutation is obtained by improving the method in the references, and relative controllability is established via Gramian criterion. Further rank criterion of a single delay system is dealt with. Simulation illustrates the theoretical deduction