Research On Maximum Delay Margin Of Time-Delay Systems

Time delay phenomenon exists widely in all kinds of actual systems. Time delay causes system instability and performance variation, so people concern widely over the delay phenomenon which will influence the performance of the system and how to eliminate or use of this influence. The stability analysis and feedback control of the time-delay systems has always been a hot problem in the study on automatic control theory.In the past few decades, It has appeared a lot of mature results about the stability of time-delay systems. But there are few results for the feedback stabilization of time-delay systems and the maximum delay margin problem, so they still need to be further studying. Many practical systems often need to feedback control to achieve stable, and time-delay in the system is often not sure, but if you can get the maximum delay margin under the action of the feedback control of the system, it will greatly reduce the complexity that we research time-delay feedback stabilization and related integrated problem. In this paper, starting from the basic method of control theory, we comprehensive utilization of frequency domain method and time domain method, study the feedback stabilization of time-delay system and the maximum delay margin problem. The concrete research content and main innovation points are as follows:In the third chapter of this paper the writer analyzes linear state feedback stabilization of time-delay systems as well as the maximum delay margin issues based on frequency domain methods. This chapter mainly has three parts:first, based on the characteristic root method and small gain theorem we get the stabilization criterion of time delay system; Second, the feedback stabilization of time-delay systems are analysed, and the algorithm of solving maximum delay margin is presented. In this part, first of all, we use the method of nonlinear singular transformation making the time-delay systems of complex quasi polynomial equation transform into simple characteristic polynomial equation, and then based on Rekasius replace getting the delay margin of stability switch time-delay system; Third, we discuss unstable poles of the system and the stable pole’s influence on the maximum delay bound.In the forth chapter of this paper the writer comprehensive use the method of time domain and frequency domain that the maximum delay margin problems are analyzed. Using Lyapunov-Krasovskii functional method and the method of integral inequality, we get the gradually stable condition of the time-delay systems. And using the matrix transformation and Schur complement lemma we convert the nonlinear matrix inequality to the form of linear matrix inequality(LMI), and convert the maximum delay margin of time-delay system into the optimal problem with linear matrix inequality constraints. We comprehensive use frequency domain method,and correlation algorithm and a numerical example is given, and a conservative analysis was carried out. The simulation results show that the proposed algorithm effectively reduces the time complexity and space complexity of the algorithm by reducing the number of iterations.