Exponential Stability And Control For Uncertain Neutral Systems With Time-Varying Delays

There exists widely the time-delay phenomenon in almost all real systems. Furthermore, time-delay is usually varying with the change of time. On the other hand, there exists all kinds of uncertainties in most partial industrial processes control systems, such as structured parametric uncertainties, change of the operating environment, model reduction and linearization approximations and external disturbances uncertainties, et al. Usually, it is much more complicated to analysis the existence of these time-varying delays and uncertainties. The study of neutral systems with time-delays becomes a hotspot and has attracted more and more researchers. Therefore, more values can be obtained from the research into the uncertain neutral systems with time-varying delays.This paper studies the exponential stability and control for the uncertain neutral systems with time-varying delays. By using the Lyapunov second method, linear matrix inequalities and matrices analysis, we will study the exponential stability, design of exponential stability robust controller, exponential stable H_∞control for the systems.The main contributions of this paper are as follows:In the first chapter, the background of this paper and state of study in the time-delay systems of neutral type are presented. In the second chapter, the corresponding preliminary information is given. In the third chapter, the exponential stability of the uncertain neutral systems with time-varying delays is studied. Based on the Lyapunov stability theory and the linear matrix inequality approach, a sufficient condition for the exponential stability for the system is presented. This sufficient condition is formulated as linear matrix inequalities. Numerical examples demonstrate the effectiveness of the proposed method. In the forth chapter, the robust control of the uncertain neutral systems with time-varying delays is studied. Through constructing proper Lyapunov function, design a linear memoryless state feedback controller so that the closed-loop system is exponential stable. The results are expressed in terms of linear matrix inequalities, and can be solved easily by using LMI toolbox in MATLAB. In the fifth chapter, the problem of the exponential stable H_∞control of the uncertain neutralsystems with time-varying delays is considered. The purpose is to design a linear memoryless state feedback controller so that the closed-loop system is exponential stable and satisfy H_∞performance index for all admissible uncertainties and time-varying delays. The exponent stability of the closed-loop system without disturbance is considered. Based on this, a sufficient condition for this system with H_∞property is obtained and it is shown by a certain LMI. It can be easily solved by MATLAB toolbox. Numerical example demonstrates the effectiveness of the proposed method. In the last, this paper is summarized and some expectations of the uncertain neutral systems with time-varying delays are given.