Bounds for the Finite Horizon Cost of Markov Jump Linear Systems with Additive Noise and Convergence for the Long Run Average Cost

The paper deals with Markov jump linear system driven by wide-sense stationary noise, stabilizable in the mean square sense by linear feedback controls, which may or my not depend on the observation of the underlying Markov jump state. The main result is an evaluation that connects the finite and the long run average costs in terms of a two-sided bound for the former cost. The derived evaluation allows us to conclude straightforwardly on the existence of the long run average cost, and hence, on the existence of the optimal control solution. For given initial condition and control, the evaluation also can be faced as an error bound for the approximation of the long run average cost by associate finite-horizon costs, thus setting an initial landmark on approximation techniques