Optimal Control for Discrete-Time Markov Jump Linear Systems with Multiple Input Channels

This paper investigates optimal control problems of discrete-time Markov jump linear systems with multiple input channels and measurement outputs. For each channel, a reduced-order observer is designed to estimate the system state by using only the local output and input information. Provided that some constraints are satisfied on the initial values of the observers, the decentralized optimal controller is constructed on the infinite horizon linear-quadratic optimal control, and the closed-loop system is also shown to be mean-square stable under mild condition. As a generalization, a kind of multi-agent systems is also investigated.