Mixed H2/H∞ control of hidden Markov jump systems

In this work, we study the mixed H-2/H-infinity control for Markov jump linear systems with hidden Markov parameters. The hidden Markov process is denoted by (theta(k), (theta) over cap (k)), where the nonobservable component theta(k) represents themode of operation of the system, whereas (theta) over cap (k) represents the observable component provided by a detector. The goal is to obtain design techniques for mixed H-2/H-infinity control problems, with the controllers depending only on the estimate (theta) over cap (k), for problems formulated in 3 different forms: (i) minimizing an upper bound on the H-2 norm subject to a given restriction on the H-infinity norm; (ii) minimizing an upper bound on the H-infinity norm, while limiting the H-2 norm; and (iii) minimizing a weighted combination of upper bounds of both the H-2 and H-infinity norms. We propose also new conditions for synthesizing robust controllers under parametric uncertainty in the detector probabilities and in the transition probabilities. The so-called cluster case for the mixed H-2/H-infinity control problem is also analyzed under the detector approach. The results are illustrated by means of 2 numerical examples.