Distributed Prescribed-Time Unknown Input Observer for LTI Systems With Event-Triggered Communication

This article studies the event-triggered prescribed-time distributed observer network design problem of linear time-invariant systems subject to unknown input (UI), where each observer node has access only to partial output information of the target system. The issue of the prescribed-time distributed event-triggered state estimation has not been adequately addressed. To this end, a novel prescribed-time distributed unknown input observer (PTDUIO), featuring the periodic delayed terms and prescribed-time coupling gain, is proposed under the scenario of continuous-time communication. It is analytically proved that the constructed PTDUIO enables each observer node to reconstruct the target system's states in the prescribed settling time regardless of initial conditions, with completely eliminating the influence of UI. To reduce the communication frequency among neighboring nodes, an improved event-triggered mechanism with the triggering condition related to the prescribed-time function is designed. Such a design facilitates the simultaneous realization of prescribed-time convergence and event-triggered communication. In addition, the sufficient criterion is derived to achieve the practical prescribed-time distributed state estimation in the event-triggered communication fashion, and the Zeno behavior is excluded. Finally, numerical examples are provided to demonstrate the effectiveness and superiority of the designed PTDUIO.