Finite Horizon Optimal Control of Markov Jump Linear Systems with Multiple State Delays

This paper investigates the optimal control for discrete-time Markov jump linear systems with multiple state delays. Necessary and sufficient condition for the finite horizon optimal control admitting a unique solution is given. Under this condition, the optimal feedback control and the optimal cost are presented via a set of coupled difference Riccati equations (CDRE). Our approach is based on the stochastic maximum principle. The key technique is to establish the relation between the costate and the state.