Riccati Design for Synchronization of Discrete-Time Systems

Abstract

In this chapter, design methods are given for synchronization control of discrete-time multi-agent systems on directed communication graphs. The graph is assumed to have fixed topology and contain a spanning tree. 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. A method is given that decouples the design of the synchronizing feedback gains from the detailed graph properties. It is based on computation of the agent feedback gains using a local Riccati equation design. Conditions are given for synchronization based on the relation of the graph eigenvalues to a bounded circular region in the complex plane that depends on the agent dynamics and the Riccati solution. The notion of ‘synchronization region’ is used. Convergence to consensus and robustness properties are investigated. This chapter also investigates the design of distributed observers for identical agents using a local Riccati design. A cooperative observer design guaranteeing convergence of the estimates of all agents to their actual states is proposed. The notion of a convergence region for distributed observers on graphs is introduced.