Optimal stabilizing controllers for discrete-time linear systems with Markovian jumping parameters under state measurements

This paper studies the average cost problem for Markov jump linear system with observation of the jump variable, considering a quite general setup for the Markov chain, allowing for non-ergodic and periodic chains for example. A dynamic controller structure is taken into account, which can be computed quite easily based on the solution of two coupled algebraic Riccati equations. We consider the cases of perfect state measurements and imperfect state measurements (noisy observation of the variable x), leading respectively to a zero order controller and a controller with the dimension of its state space. A numerical, academic example is included to illustrate the results.