LQG Control for Markov Jump Linear System with Input Delay

This paper studies the linear quadratic gaussian (LQG) control for Markov jump linear system (MJLS) with input delay. Two cases are considered here: the one-step input delay case, and the d-step input delay case (special case). The main contribution is that an extended version of the maximum principle which is applicable to the MJLS with input delay and additive noise is developed. And the LQG controllers for case 1 and case 2 are obtained by solving two sets of coupled difference Riccati equations (CDREs). No state augmentation is required herein.