Synchronizing region approach to identical LTI system state synchronization distributed control

This paper surveys some recent results in identical system state synchronization. Design methods are given for distributed synchronization control of continuous and discrete-time multi-agent systems on directed communication graphs. The graph properties complicate the design of synchronization controllers due to an interplay between the eigenvalues of the graph Laplacian matrix and the required stabilizing gains. Methods given herein are based on computation of the local control gains using Riccati design. Conditions are given for synchronization relying on relation of the graph Laplacian eigenvalues to a region in the complex plane that depends on agent dynamics and Riccati solutions. Distributed observers for agents networked on a directed graph are also investigated. Cooperative observer design guaranteeing convergence of estimates of all agents to their actual states is proposed. It is shown that the discrete-time synchronizing region is inherently bounded, so that the conditions for observer convergence and state synchronization are stricter than results for their continuous-time counterparts. If outputs only are available for control the distributed static output-feedback (OPFB) control can be used. The synchronizing region for static OPFB control is exposed and found to be conical, different than the infinite right-half plane synchronizing region for distributed state-feedback. Furthermore, the multi-agent system synchronization with control signal delays is presented. Agents are assumed to have the same control delay. Delay-dependent synchronizing region is defined and methods are given guaranteeing its estimates.