A New Method for the H₂ Problem of Hidden Markov Jump Linear Systems

This paper addresses the discrete-time H2 static state feedback control of linear systems whose parameters are governed by a hidden Markov chain. We propose a new method for designing controllers by reformulating the system using a cluster observation Markov chain (rather than a hidden one), allowing us to adapt previously existing results to the present control problem. We present numerical examples and comparisons with a baseline method, indicating that the method given here is competitive; for instance, we obtain smaller norms in 55.3% of one thousand randomly generated examples, and the norm was reduced by at least 10% in 10.0% of the cases.