# Kristian Hengster-Movric: Synchronizing Region Approach to Identical LTI System State Synchronization Distributed Control - Continuous and discrete-time systems, state, output-feedback and delays

Friday control theory seminar. Starts as usual: 2pm at K14. Open to anyone, even interested students and colleagues from other departments.

This talk surveys recent results in identical system state synchronization. Design methods are given for 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 the interplay between the eigenvalues of the graph Laplacian matrix and the required stabilizing gains. The presented methods are based on computation of the local control gains using Riccati design. Conditions are given for synchronization based on the relation of the graph 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 the estimates of all agents to their actual states is proposed. It is shown that the discrete-time synchronization region is inherently bounded, so that the conditions for observer convergence and state synchronization are stricter than the 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. In that case agents are assumed to have the same control delay. Delay-dependent synchronizing region is defined and methods are given guaranteeing its estimates.