Robust partial sampled-data state feedback control of Markov jump linear systems

Rafael F. Cunha, Gabriela W. Gabriel and José C. Geromel

International Journal of Systems Science, 2019, vol. 50, issue 11, 2142-2152

Abstract: This paper proposes new conditions for the design of a robust partial sampled-data state feedback control law for Markov jump linear systems (MJLS). Although, as usual, the control structure depends on the Markov mode, only the state variable is sampled in order to cope with a specific network control structure. For analysis, an equivalent hybrid system is proposed and a two-point boundary value problem (TPBVP) that ensures minimum $\mathcal {H}_\infty $H∞ or $\mathcal {H}_2 $H2 cost is defined. For control synthesis, it is rewritten as a convex set of sufficient conditions leading to minimum guaranteed cost of the mentioned performance classes. The optimality conditions are expressed through differential linear matrix inequalities (DLMIs), a useful mathematical device that can be handled by means of any available LMI solver. Examples are included for illustration.

Date: 2019
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DOI: 10.1080/00207721.2019.1647305

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