Research On Stability For Time Delay Systems

Due to ageing of component and mechanical wear, the measurement signal transmission of control system may produce delay. The time delay is often an important source of instability. In the control system which is complicated, requiring the control precision and high cases, the impact of delay on system stability is very great. The prevalence of the phenomenon to the delay caused a lot of practical engineering problems. Therefore, the stability analysis for time delay systems, not only can accurately master the current state of the system, but also could be an important basis for performance control.In this paper, the stability of some typical time-delay systems is studied. On the basis of investigating of a large number of domestic and foreign references, we obtain the system's stability criterion. It not only facilitates the application and has less conservative. The first chapter introduces the basic information about time-delay systems and the current domestic and foreign scholars research for delay systems, and summarizes several common useful methods. The second chapter studies the stability of linear time-delay systems. By constructing a new Lyapunov functional, using free weight matrix method, we derive stability criteria, which is in terms of linear matrix inequalities. Finally, compared with existing results, numerical examples show that the proposed approach is effective and feasible. The feasible solutions of matrix inequalities are given, and the system is simulated. The third chapter discusses the robust stability of delay systems with nonlinear perturbation. At first, interval delay systems and delay systems with nonlinear perturbation are studied. Based on taking advantage of the information, different structure for different Lyapunov functional, we obtain the robust stability of delay-dependent stability conditions. And then the robust stability of mixed delays and nonlinear neutral delay systems presents. For those neural systems, Lyapunov functional is constructed by adding the cross-term relationship of many variables. The stability of Lurie systems with a time delay are studied in the fourth chapter. It is discussed under both infinite sector and finite sector conditions. A new method of delay fraction is used in constructing a new Lyapunov functional. Combining with the way of integral inequality, then we obtain a more effective and less conservative stability criteria.