The L_2-L_{\infinity} Control for Leader-following Coordination with Switching Topology

Abstract

In this paper, we investigate the L_2-L_{\infinity} leader-following coordination problems with undirected switching topologies and external disturbance. The agent dynamics is expressed in the form of a second-order model and the control laws are neighbor-based feedback laws. We first establish a LMI sufficient condition to guarantee that all following agents can track the leader agent and the L_2-L_{\infinity} disturbance attenuation of the system is not greater than a given constant. Furthermore, we get a explicit estimation expression of L_2-L_{\infinity} disturbance attenuation by constructing a parameter-dependent common Lyapunov function. Finally, a numerical example is provided to illustrate the effectiveness of our results.