| Summary: | The problem of <inline-formula> <tex-math notation="LaTeX">$l_{2} - l_\infty $ </tex-math></inline-formula> controller design for a class of discrete-time descriptor systems is addressed in this paper. In other words, the controller is designed to ensure the admissibility and the prescribed <inline-formula> <tex-math notation="LaTeX">$l_{2} - l_\infty $ </tex-math></inline-formula> performance for the descriptor control system. The <inline-formula> <tex-math notation="LaTeX">$l_{2} - l_\infty $ </tex-math></inline-formula> performance analysis and the feedback controller design of the descriptor control system are studied by the matrix inequality technique. Novel design conditions of the feedback controller for the descriptor systems are introduced in terms of linear matrix inequality (LMI) representations. An RC circuit is applied to explain the effectiveness of the proposed <inline-formula> <tex-math notation="LaTeX">$l_{2} - l_\infty $ </tex-math></inline-formula> control design method.
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