Design of reduced-order H∞ controller for uncertain discrete system based on observer

A reduced-order H_∞ controller was studied for a discrete system based on LMI. Firstly, the existent condition of a state feedback H_∞ controller was proposed for the uncertain discrete system. And a reduced-order observer was designed to make the error between the output of the controller and the output of the state feedback controller to zero based on Sylvester equations, which controls the system to satisfy the H_∞ performance by linear matrix inequality. The approach is easy to deal with the limit of Sylvester equations in designing reduce-order controller. And a numerical example shows the feasibility of the proposed design approach.