Numerical solution for linear-quadratic control problems of Markov jump linear systems and weak detectability concept

A method for solving the linear-quadratic problem of Markov jump linear systems is developed in this paper, relying on the assumption of weak detectability. The concept of weak detectability generalizes previous concepts relevant to this class of systems, and most importantly, it allows us to revisit the quadratic control problem. In the main result of the paper, we show that, for weakly detectable systems, the solution obtained with the new method converges to the solution of the coupled algebraic Riccati equation that arises in the control problem if and only if the system is mean-square stabilizable. The paper shows how the concepts and the method involved are applied by means of numerical examples and comparisons.