H2/H∞ control problem for stochastic delay systems with multiple decision makers

In this paper, the H₂/H_∞ control problem with multiple decision makers for stochastic delay systems is considered. The H₂/H_∞ control problem is defined by reformulating the stochastic bounded real lemma and establishing the worst-case 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.