This paper is concerned with the problems of $H_{\infty }$ performance analysis and controller design for singular Markovian jump systems (SMJSs). The derivative-term coefficient is considered to be mode-dependent in SMJSs. For SMJSs with mode-dependent derivative-term coefficient $E_i,$ some extended lemmas are developed to obtain three equivalent versions of bounded real lemma. Based on a bounded real lemma, a new $H_{\infty }$ controller design condition for the closed-loop system to be stochastically admissible is formulated in the framework of linear matrix inequalities (LMIs). A numerical example is illustrated to demonstrate the effectiveness of the achieved results.

中文翻译：

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有界真实引理和 $H_{\infty }$ 与模相关的导数项系数的奇异Markovian跳跃系统的控制

本文关注的问题是 $H_{\infty }$马尔可夫跳跃系统（SMJS）的性能分析和控制器设计。在SMJS中，导数项系数被认为与模式有关。对于具有依赖于模式的导数项系数的SMJS${Ë}_{\mathrm{一世}}，$开发了一些扩展引理以获得有界实引理的三个等效版本。基于有界实引理，$H_{\infty }$在线性矩阵不等式（LMI）的框架内制定了闭环系统随机允许的控制器设计条件。数值例子说明了所获得结果的有效性。