Mixed H 2 / H ∞ control of hidden Markov jump systems

Summary In this work, we study the mixed H 2 / H ∞ control for Markov jump linear systems with hidden Markov parameters. The hidden Markov process is denoted by ( θ ( k ) , θ ^ ( k ) ) , where the nonobservable component θ( k ) represents the mode of operation of the system, whereas θ ^ ( k ) represents the observable component provided by a detector. The goal is to obtain design techniques for mixed H 2 / H ∞ control problems, with the controllers depending only on the estimate θ ^ ( 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 ∞ norm; (ii) minimizing an upper bound on the H ∞ norm, while limiting the H 2 norm; and (iii) minimizing a weighted combination of upper bounds of both the H 2 and H ∞ 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 ∞ control problem is also analyzed under the detector approach. The results are illustrated by means of 2 numerical examples.