Infinite Horizon H2/H∞ Control for Discrete-Time Mean-Field Stochastic Systems

Abstract

In this paper, we deal with the H2/H∞ control problem in the infinite horizon for discrete-time mean-field stochastic systems with (x,u,v)-dependent noise. First of all, a stochastic-bounded real lemma, which is the core of H∞ analysis, is derived. Secondly, a sufficient condition in terms of the solution of coupled difference Riccati equations (CDREs) is obtained for solving the H2/H∞ control problem above. In addition, an iterative algorithm for solving CDREs is proposed and a numerical example is given for verification of the feasibility of the developed results.