$H_2$ dynamic output feedback control for hidden markov jump linear systems

International audienceIn this note, we discuss the design of H2 dynamic output feedback controllers for a class of jump systems whose switching is induced by a Markov chain. The observation model is based on hidden Markov chains, in which only a random variable conditioned on the jump process of the plant is available to the controller. In this context, we consider a type of sub-optimal ad hoc separation procedure in which a state-feedback controller is given in order to obtain the remaining controller matrices by means of the linear matrix inequality formulation. In the case of perfect observation of the Markov chain, the conditions also become necessary allowing us to calculate optimal H2 controllers also provided by the classical results of the literature. Clusterized and mode-independent controllers can also be synthesized via our formulation. Two illustrative examples are presented