Nash strategy for Markov jump stochastic delay systems

Nash games for a class of linear time-delay system with Markovian jumping parameters are investigated. By using a classical Lyapunov-Krasovskii method and a non-convex optimization approach as a sufficient condition, a strategy set in terms of matrix inequality is established. In order to obtain a strategy set numerically, new cross-coupled stochastic algebraic equations (CSAEs) are given based on Karush-Kuhn-Tucker (KKT) conditions. Furthermore, it is shown that the state feedback strategies can be obtained by solving linear matrix inequalities (LMIs) iteratively. Finally, a numerical example is detailed that shows the effectiveness of the proposed methods.