Distributed control of networked Lur’e systems

In this thesis we systematically study distributed control of networked Lur'e systems, specifically, robust synchronization problems and cooperative robust output regulation problems. In such nonlinear multi-agent networks, the model of each agent dynamics is taken as a Lur'e system that consists of a nominal linear dynamics with a (possibly unknown) static nonlinearity around it. We generalize the standard slope-restrictedness condition to so called incremental passivity and incremental sector bounedness assumptions for Lur'e-type nonlinearities. For the interconnection topologies among these Lur'e agents, we consider two cases. One is that it is undirected and connected; the other is that the interconnection topology is directed and contains a directed spanning tree. In both cases, the interconnection topologies are time-invariant. The synchronizing protocols we design can be divided into static relative state feedback protocols, dynamic relative output feedback protocols, dynamic state feedback protocols, and dynamic output feedback protocols. Heterogeneous Lur’e agents as well as identical ones are discussed. Besides robust and H-infinity control, output regulation theory is employed. All the results are illustrated by numerical simulation examples. In addition, all the material in this thesis deals with continuous-time systems.