H∞ Constrained Pareto Suboptimal Strategy for Stochastic LPV Time-Delay Systems

Not only in control problems, but also in dynamic games, several sources of performance degradation, such as model variation, deterministic and stochastic uncertainties and state delays, need to be considered. In this paper, we present an H∞ constrained Pareto suboptimal strategy for stochastic linear parameter-varying (LPV) time-delay systems involving multiple decision makers. The goal of developing the H∞ constrained Pareto suboptimal strategy set is to construct a memoryless state feedback strategy set, so that the closed-loop stochastic LPV system is stochastically mean-square stable. In the paper, the existence condition of the extended bounded real lemma is first established via linear matrix inequalities (LMIs). Then, a quadratic cost bound for cost performance is derived. Based on these preliminary results, sufficient conditions for the existence of such a strategy set under the H∞ constraint are derived by using cross-coupled bilinear matrix inequalities (BMIs). To determine the strategy set, a viscosity iterative scheme based on the LMIs is established to avoid the processing of BMIs. Finally, two numerical examples are presented to demonstrate the reliability and usefulness of the proposed method.