A Study On The Uncertainituy Time Delay System By Robust Control Theory

In the process of industry, the system of uncertainty widely exist ,such as, dynamic modeling, the uncertainty of the parameters'structure and the uncertainty of the outside disturbances. All these uncertainties are difficult to measure. So people usually can only give these uncertainties some constraints. However, the Robust Control theory is one of the best methods to solve these uncertainties. On the other hand, in many industrial production processes, the time delay system is a common phenomenon, especially in larger size industrial device. As in these devices, this phenomenon is difficult to be avoided. It is due to come up the delay phenomenon in industry transmission, complex linear analysis, and petrochemical and metallurgical industries producing processes. The delay phenomenon has serious impact on the control system's stability and performance index. Therefore, the control system stability problems, especially time delay system stability and its performance index come to be the important research subject of control theory. This research mainly focuses on the problems of uncertainty time delay system's Robust Control. By using matrix theory of linear matrix inequality, and Lyapunov theory and so on to deal with the following questions :1. On the linear uncertain time delay system, such as x(t)=Ax(t)+ A₁x(t-Ï„) system, the research gives a necessary and sufficient condition to the certainty of the system in the matrix inequality form. On this base, the research extends its stability judgment conditions. At last, the research gives number examples to prove its validity.2. On the linear uncertain time delay system, such as x( t) = A₀ x( t) + B₀ u( t) + A₁ x( t-d )+ B₁ Fx(t-h) + Dw (t ) system, this research gives some situation time delay system and input linear time delay system of Robust stable devices, some judgment and still some approached to the closed system stability and good condition.3. On the linear uncertain time lag system, this research does some studies on the insurance cost control.