Neutral Delay Systems Stability And Control

The time-delay systems exist widely in real world, the existence of the time-delay makes the stability analysis much more complicated. The study of the system stability is an important area in the dynamical system theory. The stability is not only basic demand of the dynamical system, but also necessary precondition of keeping system in gear. The study of the time-delay systems of neutral type became a hotspot and had attracted more and more researchers. These systems contain not only information of the past state but also information of the derivative of the past state. These systems can be depicted by the differential function of neutral type. The study of the neutral systems will offer better theoretical basic and means for dealing with practice.This paper studied stability and H control problems of the neutral time-delay systems by using Lyapunov second method. By constructing Lyapunov founctional, using linear matrix inequality and matrices analysis, stability criterion and H∞ controller of the neutral time-delay systems were given. The main works as following:In the first chapter, the problem background of this paper and the state of study in the time-delay systems of neutral type were presented. In the second chapter, the stability problem of the neutral systems with single time-delay and multiple time-delays was studied. Based on Lyapunov second method, the system asymptotic stability criterions were given in terms of linear matrix inequalities through using an improved inequality. The criterions are delay-dependent and have less conservation compared with time delay-independent criterions. Numerical examples indicate that the criterions expressed in this chapter have significant improvements over some existing results, and easier to use. The asymptotic stability of the neutral systems with distributed delay was considered in the third chapter. The time-delay systems of neutral type with distributed delays have more broad representation. The main results were expressed in terms of linear matrix inequalities through deforming system equation identically and constructing proper Lyapunov functional. The results can be solved easily by using LMI toolbox in MATLAB. The neutral systems with time-varying delays were also taken into account in the fourth chapter. The sufficient delay-dependent stability criterions were expressed. The results obtained can be expended to systems with multiple time-varying delays. In the fifth chapter, the robust H∞ control of the uncertain neutral time-delay systems was studied. First H∞ controller for normal neutral time-delay systems was designed. Based on these, robust H∞ control of the uncertain neutral time-delay systems was studied. The results are expressed in terms of linear matrix inequalities. Numerical example indicates that the results are available and easier to use. In the last, we sum up this paper and give some expectations of the neutral time-delay systems study.