Finite-Horizon $$H_{\infty }$$-Consensus Control for Multi-agent Systems with Random Parameters

Abstract

In this chapter, the finite-horizon distributed H $$\infty $$ -consensus control problem is addressed for a class of discrete time-varying multi-agent systems with random parameters and missing measurements via the local performance analysis method. With the aid of the assumption that the considered topology has a spanning tree, it is proved that the local consensus based on the information among neighboring agents is equivalent to the global consensus described by any two agents. Then, a novel dynamic local H $$\infty $$ -consensus performance index are proposed just considering the consensus error among neighboring nodes to cater for the requirement of local performance method. The WCM formula of random matrix involving the covariance information between any two random variables is established via the Kronecker product and the Hadamard product. A set of locally coupled sufficient conditions for every agent has been obtained such that the proposed locally dynamically H $$\infty $$ -consensus performance constraints are satisfied in the presence of the external disturbances. In addition, the explicit expressions of the desired controller gains are obtained.