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In this technical note, H∞control problem of continuous Markovian jump systems is investigated. A linear feedback control scheme, combined with a state observer design, is proposed in the form of linear matrix inequalities, which can ensure the systems' mean-square stability with H∞performance. Then, a multi-step state transition conditional probability function is introduced for the continuous Markovian process, which is used to define the system's mean-square stability probability. Furthermore, the formulas for calculating the mean-square stability probability are derived for situations where the control force may not be strong enough to ensure the full stability. Simulation results are presented to show the effectiveness of the theoretical results.
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Zhu et al. (2015) studied this question.
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