Stackelberg Strategy for Uncertain Markov Jump Delay Stochastic Systems

In this letter, a robust Stackelberg game for a class of uncertain Markov jump delay stochastic systems (UMJDSSs) is investigated. After introducing some definitions and preliminaries, we derive the conditions for the existence of a robust Stackelberg strategy set by means of cross coupled stochastic bilinear matrix inequalities (CCSBMIs), such that the upper bound of each decision maker's cost function is minimized. To overcome difficulties in solving the CCSBMIs, a feasible numerical algorithm based on the Krasnoselskii iteration sequence is proposed, which consists of linear matrix inequalities and cross coupled stochastic matrix equations (CCSMEs). It is shown that the weakly convergence property is attained. Finally, a practical example is solved to demonstrate the effectiveness and efficiency of the proposed scheme.