Robust H∞ Control of Markov Jump Linear Systems with Uncertain Switching Probabilities
DOI:
https://doi.org/10.22213/2410-9304-2021-2-123-128Keywords:
Markov Jump Linear Systems, Robust H Control, Linear Matrix Inequalities, Uncertain Markov ParametersAbstract
This paper the problem of robust H∞ control for Markov jump systems with uncertain transition rates is investigated. A robust H∞ performance criterion is established for a given Markov jump system. The robust H∞ control performance analysis in terms of coupled linear matrix inequalities is proposed, then convex optimization problem is solved with constraints defined in terms of the solvability of the linear matrix inequalities. Based on the solution of the optimization problem, the condition of robust stochastic stability for closed-loop systems is found, which minimizes disturbance attenuation level. Depending on the developed performance criterion, the H∞ state-feedback controller is designed too, which warranties the robust H∞ control of the closed-loop system. All the conditions are linear matrix inequalities, and therefore they can be solved by any linear matrix inequalities solver. Finally, a numerical example is given to show the effectiveness of the method of robust H∞ control for Markov jump systems.References
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