l ₂– l ∞ Control for Discrete-Time Descriptor Systems

The problem of $l_{2} - l_\infty $ 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 $l_{2} - l_\infty $ performance for the descriptor control system. The $l_{2} - l_\infty $ 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 $l_{2} - l_\infty $ control design method.