Robust static output feedback control for hidden Markov jump linear systems

This paper studies the robust static output feedback control of discrete-time Markov jump systems considering that the mode of operation cannot be directly measured. It is assumed that the only available information concerning the main jump process comes from a detector, so that the jump and detector processes can be modelled as a hidden Markov model. Initially, it is considered that the system's dynamic matrix is subject to parametric uncertainties. By assuming a full row rank condition for the output matrix and employing a clusterisation technique for the state space of the hidden Markov model, it is derived a set of linear matrix inequalities (LMIs) that guarantees robust stability in the mean-square sense of the closed-loop system, as well as a bound on its H-2 norm. It is also shown that this design technique is linked to the bounded real lemma, so that a new set of LMIs conditions can be obtained for the 'pure' H-infinity control problem, which can be extended to cover the robust polytopic case. The paper is concluded with an illustrative example.