Robust Nash Equilibrium Strategy for Uncertain Markov Jump Linear Stochastic Systems

In this paper, a novel delta-neighborhood robust Nash equilibrium strategy with disturbance attenuation for uncertain Markov jump linear stochastic systems (UMJLSSs) involving multiple decision makers is investigated. The Stackelberg game concept for the UMJLSSs is introduced to derive the hierarchical strategy set. Exploiting the theory of guaranteed cost control, the sufficient conditions such that the stochastic system is exponentially mean square stable (EMSS) and has a cost bound are established by the stochastic algebraic Riccati inequality (SARI). The optimization problem of the cost bound for a given cost function is described and it is shown that the necessary conditions based on the Karush-Kuhn-Tucker (KKT) conditions can be established by the set of cross-coupled stochastic algebraic Riccati equations (CCSAREs). Furthermore, to avoid the complex calculation for solving SARI and CCSAREs, an iterative numerical algorithm is proposed. Finally, a numerical example demonstrates the advantages and generalization of our existing results.