Finite-Time Analysis And Synthesis For Neutral Time-Delay Systems

The time-delay phenomenon often occurs in actual systems, some delays may be caused by human activities, and some may be produced in various components of the transmission process. Regardless of which factors lead to this phenomenon, it can not be ignored, since the time lag is a important factor contributing to poor system performance as well as system instability. Neutral time-delay system is a special one of time delay system; In this system, time delay terms and its derivative coexist in its functional differential equations, which makes it difficult to analyze its stability characterities. But this system is a very common model exists in various physical or engineering processes, for instance, the lossless transmission line. Therefore, the study of neutral time-delay system has both theoretical and practical significance.In recent years, many research results has been obtained by researchers in control field, and many of them are based on Lyapunov asymptotic stability. But in practical application, we focus on the track of the state and the performance of system over a fixed time interval. Finite time stable (FTS) theory, proposed by Dorato in the 1960s, is favored by researchers because it focus on this kind of problem. Later, the definition of finite-time boundedness and finite-time stabilization appeared later is also derived by the concept of finite-time stability, but few work consider the finite time theory with neutral system. In this dissertation, we apply the Lyapunov function, linear matrix inequality (LMI) technique, and the free weighting matrix method to study the finite time control problem of neutral delay system. The main result are as follows:1. For a class of uncertain neutral time-delay system, we obtain a delay-dependent finite-time stability condition based on the FTB and given the H∞ performance index.2. Considering the finite-time control theory, an output feedback controller has been designed for a class of nonlinear uncertain neutral time-delay systems; and the closed-loop system is FTB and satisfies the L2-L∞ performance constraint condition.3. A class of uncertain neutral systems with time-varying delays has been studied, and a sufficient condition for the existence of the resilient finite-time L2-L∞ controller has been obtained.