Optimal Output Feedback Control for Discrete-time Markov Jump Linear System with Multi-step Input Delays

This paper deals with the finite horizon optimal output feedback control problem for a class of discrete-time Markov jump linear system (MJLS) with multi-step input delays and additive noise. The main difficulties lie in solving a set of coupled difference Riccati equations (CDREs) with time delay terms and overcoming the influence of the invalidity of the separation principle in designing an output feedback controller. Firstly, the explicit expression of the optimal controller is derived from the maximum principle suitable for MJLS. It is shown that the optimal controller is a linear function of the current system state and the system’s historical input. Moreover, when the state is unavailable, a filter is designed by introducing an augmented system. Finally, based on the filter, an optimal output feedback controller is obtained.