H2/H∞ Control Problem for Stochastic Delay Systems with Multiple Decision Makers

In this paper, the H-2/H-infinity-control problem with multiple decision makers for stochastic delay systems is considered. The H-2/H-infinity-control problem is defined by reformulating the stochastic bounded real lemma and establishing the worstcase disturbance for the stochastic delay system. Since many decision makers exist, both the Pareto optimality and Nash equilibrium are considered for each player. The solvability conditions of the problem are derived from cross-coupled matrix inequalities. A numerical example demonstrates the validity and usefulness of the proposed strategy set.