New Results on Output Feedback $H_{\infty }$ Control for Linear Discrete-Time Systems

This note investigates the problem of output feedback H_∞ control for linear discrete-time systems. Three types of H_∞ controllers are considered, namely, static output feedback controllers, dynamic output feedback controllers, and observer-based output feedback controllers. New design conditions for the three type of output feedback controllers are introduced in terms of unified linear matrix inequality (LMI) representations, which guarantee the prescribed H_∞ performances of the closed-loop systems. In contrast to the existing LMI conditions for designing the output feedback H_∞ controllers, the improvement of the proposed results over the existing ones is shown by theoretical proof and numerical example.