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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state observer note hsubx221esub control problem of continuous markovian jump systems multistep state transition conditional probability function continuous markovian process hsubx221esub performance results systems meansquare stability probability linear feedback control scheme linear matrix inequalities

JiamingZhu, TianpingZhang, ZhiqiangCao, YuequanYang, XinghuoYu, YangYi,.The Mean-Square Stability Probability of Control of Continuous Markovian Jump Systems. 61 (7),1918-1924.

JiamingZhu, et al."The Mean-Square Stability Probability of Control of Continuous Markovian Jump Systems" 61

JiamingZhu, TianpingZhang, ZhiqiangCao, YuequanYang, XinghuoYu, YangYi,"The Mean-Square Stability Probability of Control of Continuous Markovian Jump Systems"