Cooperative Tracking of CNSs with a High-Dimensional Leader and Directed Switching Topologies

Unlike previous chapters where the leader and the followers have the same dimensional dynamics, this chapter studies the complex network systems with a single high-dimensional leader, where the cooperative goal is that the states of the followers converge to the outputs of the leader. This chapter firstly proposes a reduced-order state observer for each follower to estimate the leader's dynamics, then the consensus controller is designed. Section 9.3 firstly studies the asymptotical consensus of complex network systems without any external disturbance under directed switching topologies. Then we extend the results to the case with unknown external disturbances by showing that a finite L₂-gain performance for tracking errors against external disturbances can be ensured. At last, the synthesis issue of designing an observer-based controller to achieve a prescribed L₂-gain performance for consensus tracking is studied by using tools from H _∞ control theory, where the underlying topology is assumed to be undirected and fixed. Finally, this chapter presents some simulations to validate the theoretical results.