Containment Tracking for Networked Agents Subject to Nonuniform Communication Delays

This article examines the effect of multiple nonuniform time delays on the performance of containment tracking control for networked agent systems. At first, the distributed controllers are designed under undirected and directed interactive networks, respectively. Then, the corresponding characteristic equation of the closed-loop system is transformed into a quadratic polynomial with respect to the pure imaginary eigenvalue of the system to calculate the critical time delay. Finally, the explicit maximum allowable upper bound of time delay (called “delay margin”) for achieving containment tracking is obtained. To sum up, we tackle the containment tracking problem and obtain sufficient convergence conditions for networked agents with nonuniform communication delays, where the system can achieve containment tracking when all time delays are less than the obtained delay margin, i.e., all follower agents asymptotically converge to the convex hull formed by the leaders, and the system will not remain stable when all delays are greater than the obtained delay margin. The superiority of the obtained results is well verified by numerical examples.