The linear quadratic optimal control problem for discrete-time Markov jump linear singular systems

In this paper, we address the linear quadratic optimal control problem for discrete-time Markov jump linear singular systems. The results are obtained under conditions that bring some additional structure to the quite general and complex class of systems being considered. The approach involves base transformations and restricts the control actions into an appropriate subspace to ensure regularity of the closed-loop system. Both finite and infinite time horizon problems are considered. The results are evaluated by means of an example.