Stability Of Lurie Control System And Its Application

Lurie control system is very typical class of uncertain nonlinear control systems, whose nonlinear part is isolation as a feedback control, also a form of closed-loop control systems, and it is widely applied in practical engineering applications. All along, the research and development of system has been focused on the stability. The explore methods including some methods such as S-procedure law and popov frequency method are combined by the Second Lyapunov stability theory and give out the sufficient and necessary conditions for the Lurie control system to judge whether it is stability or not. Under the different conditions, the complexity of conclusion given out from them is not the same for the instability of the systems. If using the non-integral Lyapunov function to determine the stability of Lurie control system directly, the results will be more concise and more suited to be proceeded. However the problems how to structure the Lyapunov function against the Lurie control system , what are the characteristics and laws of these functions are very difficult to explore. But this article is elaborated in detail and lists some relevant examples to answer the questions about which is the advantages of the law, how to solve the related issues of other works of literature by this approach in the practical application.This thesis of Master is composed of three chapters which mainly discuss the structure of the matrix Bto meet certain conditions, give the stability criteria of the Lurie control system , as well as the properties of the matrix B, and used them to consider the problem ofАйзерманtheory on A, b, c parameter sets. Some examples of the practical application are given out.In chapter one, we introduce the development background and the significance of the Lurie control systems. In addition, a analysis of the relevant results from the domestic and foreign scholars is given.In the second chapter, we discuss the application and stability of the general Lurie systems, and find a method to take the sufficient conditions for them. By the structure matrix B betwem b band c of the Lurie control system, we get the construction method and laws. And combined by the second Lyapunov stability theory, we lastly have the access to the new conclusions of stability of the Lurie control system. The listed examples will show that.In the third chapter, we analyze the stability of the Lurie parameters control system, get some useful conclusions, and also present some application examples. Furthermore, we try to use this theory to Solve problems of the, and get some practical results.Finally, the summarization and conclusion about what this paper works out, and the plan of the future work are given.