Robust H∞ control based on parameters weak coupling LMI equations set for uncertain singular state delay systems

This note deals with the problems of delay-dependent robust stabilization and robust H_∞ control for uncertain singular systems. The control law is designed to guarantee that the resulting closed-loop system is regular, impulse-free and stable for all admissible uncertainties. And a prescribed H_{/pl infin/} performance is achieved in robust H_∞ control problem. This criteria is devised in terms of parameters weak coupling LMI equations set (PWCLMIES). The concept and constructing method of PWCLMIES are developed. The concept of two levels of conservatism is proposed clearly and is used to analyze the conservatism of the PWCLMIES condition, too. Large time delay, large time-varying rate and small disturbance attenuation can be obtained by using this method. At the same time, a new method which proves the system is regular and impulse-free is introduced. A numerical examples is given to demonstrate the effectiveness of the proposed criteria.