Time-varying output formation for linear multiagent systems via dynamic output feedback control

Time-varying output formation control problems for linear multiagent systems with directed interaction topologies are studied using a dynamic output feedback approach. First, a dynamic output formation protocol is constructed using the outputs of neighboring agents. Based on the output decomposition, observability decomposition and output formation decomposition, necessary and sufficient conditions for linear multiagent systems to achieve time-varying output formations are presented. An explicit expression of the output formation reference function is derived to describe the macroscopic movement of the entire output formation. Then, an algorithm with three steps is proposed to design the dynamic output formation protocol, where the gain matrices of the protocol can be determined by solving an algebraic Riccati equation. It is shown that if the dynamics of each agent is stabilizable, the solvability of the algorithm can be guaranteed. Moreover, a feasible time-varying output formation set is derived, and the stability of the proposed algorithm is proven based on the separation principle and Lyapunov stability theory. Finally, numerical simulation is presented to demonstrate the effectiveness of the theoretical results.