Prescribed-Time Bipartite Synchronization for General Linear Multiagent Systems: An Adaptive Dynamic Output-Feedback Strategy

Achieving prescribed-time synchronization with output-feedback measurements in general linear multiagent systems is challenging, as it necessitates the simultaneous achievement of state synchronization and observer estimation within a prescribed time. This article focuses on general linear dynamics and aims to solve the prescribed-time bipartite synchronization (PT-BS) problem over cooperative-antagonistic networks. First, a couple of time-varying Riccati equations (TVREs) is introduced, which transforms the prescribed-time synchronization problem into a dynamic parameter design issue. By using the solutions of TVREs to design output feedback gains, a class of time-varying-gain prescribed-time observers and observer-based protocols are proposed. Then, since the proposed PT-BS observers require knowledge of some global information (i.e., the minimum eigenvalue of the topology-relevant Laplacian matrix), two adaptive strategies are presented to solve the output-feedback PT-BS problems in a fully distributed manner: an edge-based adaptive strategy and a node-based adaptive strategy. It successfully achieves state synchronization, observer estimation, and adaptive gain convergence within the prescribed settling time. Finally, a simulation example demonstrates the effectiveness of the theoretical results.