Abstract: Based on the method of LMI， H∞ optimal control by dynamic output feedback was studied for the standard control model of the generalized system. The general solution of ETX=XTE was used for several congruent transformations and variable substitutions of the matrix in the inequality. Then the necessary and sufficient condition for the presence of the controller was given. What’s more， the design method was given for the controller. Finally， a corresponding numerical example was presented to illustrate the effectiveness of the proposed method.

Key words: descriptor systems, dynamic output feedback, H∞ optimal control, linear matrix inequality (LMI), congruent transformation, Schurcomplement