A suboptimal LMI formulation for the $H_2$ static output feedback control of hidden Markov jump linear systems

International audienceIn this work we study the synthesis of $H_2$ static output feedback controllers for Markov jump linear systems in a context of partial observation of the Markov chain. We consider a hidden Markov model in which the controller has no access to the Markov chain $\theta(k)$, but only to an observable process represented by $\xi(k)$. We present a suboptimal condition based on the so-called two-stage procedure in order to design static output feedback controllers that depend only on $\xi(k)$ such that the closed-loop system is stochastically stable and its $H_2$ norm is bounded by some given scalar γ. Our results are given in terms of linear matrix inequalities and are illustrated by a numerical example in the context of systems subject to failures