Optimal Stationary Dynamic Output-Feedback Controllers for Discrete-Time Linear Systems With Markovian Jumping Parameters and Additive White Noise Perturbations

This paper addresses stationary dynamic output-feedback control of discrete-time Markovian jumping linear systems (MJLS). A rather general setup is adopted, with indirect and noisy output measurements, infinite time horizon, and not necessarily ergodic Markov chains. The class of admissible controllers consists of all stabilizing systems, dynamic or memoryless, with arbitrary dimension. The quality of stabilization achieved by an admissible controller is measured by a performance criterion described by a long run average cost, under some standard conditions. The optimal controller can be computed off-line resting on two sets of Riccati equations and it only requires the storage of 4N matrices where N is the cardinality of the Markov state space. We present an example of a quad-rotor system to illustrate the results and compare the performance of three different control schemes with the proposed one, indicating that it is an interesting, simple alternative for controlling MJLS. Although the systems under consideration are subject to random perturbations, the proof of the main result is based on arguments typical of deterministic systems.