Markovian jump linear quadratic optimal control in discrete time

This paper is concerned with the optimal control of discrete time linear systems that possess randomly jumping parameters described by finite state Markov processes. For problems having quadratic costs and perfect observations the optimal control laws and expected costs-to-go can be precomputed from a set of coupled Riccati-like matrix difference equations. Necessary and sufficient conditions are derived for the existence of optimal constant control laws which stabilize the controlled system, as the time horizon becomes infinite, with finite optimal expected cost.