Observer-based guaranteed-cost bipartite time-varying formation tracking control for multiagent systems subject to communication delays

The paper centers on the guaranteed-cost bipartite time-varying formation tracking control for multiagent systems with nonuniform time-varying communication delays under the framework of a distributed observer. An integral quadratic cost function is presented, founded on formation tracking and observation error. Firstly, distributed state observers, using the relative measurement output between neighbors, are established so that the leader and follower can accurately estimate each agent's unmeasurable state. Subsequently, a bipartite formation tracking protocol is proposed, incorporating estimation information and nonuniform time-varying communication delays. This protocol aims to achieve bipartite time-varying formation tracking for multiagent systems. Next, a new augmented Lyapunov-Krasovskii functional with delay-product and triple integral terms is constructed. By integrating the second-order Bessel-Legendre inequality technique, the delay-dependent reciprocally convex combination inequality method, and the free weight matrix technique, a new guaranteed-cost bipartite time-varying formation tracking criterion is developed, offering less conservatism. Compared to certain existing delay conditions, the stability conditions assure a greater allowable upper bound of delay. Finally, a numerical example is conducted to confirm the validity and superiority of the theoretical findings.