Fully distributed prescribed-time bipartite synchronization of general linear systems: An adaptive gain scheduling strategy

Investigating the prescribed-time synchronization problem for multiple linear agents is challenging because the states and inputs of the system are coupled through the state-input matrix pair. To address this challenge, this paper develops a gain scheduling strategy for linear multi-agent systems over a cooperative-antagonistic network. First, the strategy converts the problem to a time-varying parameter design problem using a time-varying parametric Lyapunov equation (TVPLE). By exploiting the time-varying solution to TVPLE for designing the feedback gains, prescribed-time bipartite synchronization protocols are designed for systems over undirected and directed networks, respectively. These protocols require some global information; therefore, edge- and node-based adaptive gain scheduling strategies are further developed to achieve the prescribed-time bipartite synchronization in a fully distributed manner, which guarantees simultaneous convergence of both state synchronization and adaptive gains within a prescribed time. Finally, a simulation example is presented to demonstrate the effectiveness of the designed adaptive protocols.