Control for continuous-time Markovian Jumps Linear Systems associated with a finite number of jump times

The continuous-time Markov Jump Linear Systems (MJLS) are defined as a family of linear systems with randomly jumping parameters governed by a continuous-time Markov jump process and usually used to described systems subject to failures or changes in structure. The MJLS have been studied extensively since the work of Krasovskii and Lidskii [1]. Regarding stability conditions, optimal control problems and applications, see for instance [2], [4], [5], [6] and the references therein. In particular, a significant effort has been devoted to the Jump Linear Quadratic (JLQ) optimal control problem. Under the assumption that the process state is available to the controller, the solution of JLQ control problem was developed in [2] and [3], [4], [5] for finite and infinite horizon cases, respectively.