Nash Linear Quadratic Game by State Feedback for Linear Discrete-Time Markovian Jump Systems

Abstract

In this paper, we study Nash game problems for linear discrete-time Markovian jump systems over finite time intervals. We introduce double coupled difference equatuons (CDREs) to give solutions of the game problems with multi-players. Using these solutions, we obtain Nash strategies by state feedback. In this paper, we focus on the derivation of the necessary conditions for the solvability of the game problems by variational approach.