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\(\mathcal{H}_2\) detector-based state feedback control of continuous-time MJLS subject to uncertain transition rate matrices. (English) Zbl 07919281

Summary: This paper uses detector-based mode information to address the \(\mathcal{H}_2\) state-feedback control problem for continuous-time Markov Jump Linear Systems (MJLS). The focus is on designing robust controllers capable of handling uncertainties affecting both the Markov process and its detector, a less explored scenario in the literature. The main contribution lies in presenting a new LMI-based algorithm within a suitable synthesis framework to deal with uncertain parameters. A key advantage is the absence of constraints on the optimization variables, even in cases involving structured controllers like decentralized control. To illustrate the effectiveness of the proposed technique, a numerical example based on a linearized model of an unmanned aircraft is provided, showcasing its superiority over existing approaches.

MSC:

93E03 Stochastic systems in control theory (general)
93B52 Feedback control
93C30 Control/observation systems governed by functional relations other than differential equations (such as hybrid and switching systems)
93D15 Stabilization of systems by feedback
93E15 Stochastic stability in control theory

Software:

Mosek
Full Text: DOI

References:

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