On the delay bound for coordination of multiple generic linear agents under arbitrary topology with time delay

A coordination control of multiple generic linear homogeneous agents under arbitrary network topology with uniform and fixed time delay is proposed in this paper. From the network topology, the agents are categorized into two groups: those within the closed strong components (group 1) and those outside the closed strong components (group 2). It is shown that under allowable delay bound, the agents of group 1 reach synchronization while the agents of group 2 converge asymptotically to the convex hull spanned by the synchronized agents of group 1. The technique of semi-discretization is applied for computing the delay bound. For a specific time delay, the method is also feasible in finding an optimal coordination control gain with the fastest decay rate. A linear matrix inequality method is also given to show an alternative way to find the maximum allowable delay bound. An illustrative simulation is presented to validate our obtained theoretical results.