H∞ Consensus Control for Discrete-Time Stochastic Multi-agent Systems with Infinite Markov Jumps

Abstract

This paper focuses on multi-agent systems under the disturbances of parameter uncertainties, noises and external disturbances simultaneously, which are more suitable for the changing environments than most ideal models. For this case, the robust H∞ consensus control problem is studied to attenuate the influence of disturbances below a given level. We aim to design a consensus controller such that the closed-loop muti-agent systems reach the desired H∞ performance. By tools of Kronecker product, graph theory, and infinite horizon bounded real lemma, sufficient conditions for existence of H∞ consensus protocol design are obtained in terms of linear matrix inequalities (LMIs). Finally, a numerical example is given to show the validity of the method.