Stability of receding horizon control of Markov jump linear systems without jump observations

This paper addresses the stability of receding horizon control for discrete-time Markov jump linear systems assuming no observation on the jump variable and complete observation of the linear state. Linear feedback is employed, and it is shown that the quadratic N-stage cost functional provides a test for the stability in the mean square sense. The resulting stability condition relies on the idea of a sufficient large horizon length and an observability concept is developed to assure the existence of such an horizon.