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Design of robust H_∞ controller for a class of uncertain singular systems with time-delay

LI Wen-zi,WU Bao-wei(Coll. Math. & Infom. Sci., Shaanxi Normal University, Xi'an 710062, Shaanxi, China)  
Aim To study the robust H∞ control problem of a class of uncertain singular systems with matched and unmatched uncertainties and time-delay.Methods Lyapunov function is constructed and properly enlarging inequality,problems are solved by LMI techniques.Results The condition of quadratic stabilization is given and the H∞ performance of the systems is analyzed and designed for all admissible uncertainties.The robust H∞ controller which satisfies not only quadratic stabilization but also H∞ performance is developed. A numerical example is given to demonstrate the effectiveness and feasibility of the controller.Conclusion Decide whether the system satisfies the condition of quadratic stabilization and the H∞ performance or not by LMI, and design its H∞ controller,which is simple. Moreover, the results provided here generalized the corresponding results in references.
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