| Summary: | This paper addresses the robust finite-time <inline-formula> <tex-math notation="LaTeX">$H_\infty $ </tex-math></inline-formula> control problem for the uncertain singular system by using the stability theory of dynamical systems. Firstly, a lemma is provided to show that the singular system is finite-time stability by using the state space decomposition approach. Similar with the proof method of this Lemma, the singular system is divided into a differential system and an algebra one. Then, some conditions are derived to ensure the singular system being finite-time <inline-formula> <tex-math notation="LaTeX">$H_\infty $ </tex-math></inline-formula> stability based on the obtained lemma, and the state feedback control law is designed. These conditions are provided in the form of the linear matrix inequalities and can be easily solved. Finally, a numerical example is given to illustrate the effectiveness of the obtained results.
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