Robust static output feedback control for hidden Markov jump linear systems

A. M. de Oliveira, O. L. V. Costa and G. W. Gabriel

International Journal of Systems Science, 2022, vol. 53, issue 6, 1298-1316

Abstract: 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} $ H2 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_\infty $ H∞ control problem, which can be extended to cover the robust polytopic case. The paper is concluded with an illustrative example.

Date: 2022
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DOI: 10.1080/00207721.2021.1999532

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