A Class Of Uncertain Linear Discrete Time Delay Singularly Perturbed System Robust Control And Guaranteed Cost

Singular perturbation theory not only has developed rapidly in the area of mathematics, but also has made a number of breakthroughs in the area of analysis and synthesis of control processes in the past half a century. Studying the singular perturbation theory is of great significance in both the theory and the engineering. In addition, the linear matrix inequality (LMI) approach has been widely used in solving the singularly perturbed control problems. Many results have been obtained by LMI's applications in singular perturbation theory. However, up to the present, the problem of robust control for singularly perturbed systems through LMI approach has not solved perfectly. Considering this, in this dissertation, attention is focused on solving the control problems for a tape of polytopic uncertain fast discrete time-delay singularly perturbed system through linear matrix inequality approach and Lyapunov stability theorem. The main results obtained in this paper are as follows:(1) This dissertation gives a sufficient condition to stable discrete singular perturbation system of above. Then it designs a memoryless state feedback controller for the system, making it asymptotically stable in the form of the closed-loop system. In other words, the stabilization robust problem of the open loop system is analyzed.(2) In view of the above discrete singular perturbation system with state-delay and input-delay, the paper gives a robust H∞controller irrelevant to delay and perturbed parameters, followed by finding out the applicable perturbation parameter range of the controller.(3) At last, the guaranteed cost control of the above discrete singular perturbation system is investigated, and a robust H∞guaranteed cost controller irrelevant to delay and perturbed parameters is designed. So that, the researched system is not only the gradual stable but meets a certain H∞performance index under the action of the controller. What's more, the given cost function is not beyond an upper bound.