This work is concerned with the H_∞ state‐feedback control for the discrete‐time Markovian jump systems with incomplete knowledge of transition probabilities. A less conservative criterion is proposed via linear matrix inequalities (LMIs) such that the considered systems are stochastically stable and have a prescribed H_∞ disturbance attention level. Furthermore, based on the obtained results, a state‐feedback controller is presented via LMIs to guarantee the stochastic stability of the resulted closed‐loop system with a prescribed H_∞ performance level γ. The number of the LMIs to be solved in the developed methods is much less than that in many existing methods. A numerical example and a practical example are provided to verify the effectiveness of the presented methods.

中文翻译：

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具有部分不确定转移概率的离散时间马尔可夫跳跃线性系统的H∞控制

这项工作涉及的^ h _∞与转移概率的不完整的知识离散时间马尔可夫跳变系统的状态反馈控制。不太保守的标准，提出了经由线性矩阵不等式（LMI），使得所考虑的系统是随机稳定和具有规定ħ _∞干扰注意力水平。此外，基于所获得的结果，一个状态反馈控制器通过线性矩阵不等式给出，以保证所得到的闭环系统的随机稳定性与规定ħ _∞性能水平γ。在开发的方法中要解决的LMI数量远少于许多现有方法中的LMI数量。数值算例和实例算例验证了所提方法的有效性。