Abstract: Aiming at resolving relevant problems occurring in a classification of uncertain singular systems with multiple－states time－varying delays, a sufficient condition for the closed－loop system that is quadratically stable is presented by solving the linear matrix inequality. In addition, a condition for the given systems with memoryless quadratical stabilization and H∞ properties is presented in terms of a certain linear matrix inequality, and the designing method of the Robust H∞ controllers is obtained by solving the LMI.

Key words: time－delay systems, LMI, linear matrix inequality, H∞ properties