Types Of System With Delay And Of H_ ¡Þ Control

In physical phenomenon, the present state depends on the past. This character is commonly known as time-delay. The system with time-delay is called time-delay system. Time-delay always exist in kinds of practical industry systems. For example, the feed stock of deeper pipelining, belt transmission, complex on line analyser. The transmission of messages or materials in systems also generate time-delay. For example, electrical systems, chemical systems and communication systems. They are all typical time-delay systems. In the process of produce, the environmental change in systems and physical parameters lead to the uncertainty in systems. The existence of time-delay phenomenon and uncertainty in systems made the analysis and comprehensive very difficult in systems. It also lead to instability in systems and the decline of performance index. The problem of H∞control is to get a controller to make the closed-loop system asymptotically stable and get the minimum value of transfer matrix which is from disturbance input to control output. So, it is necessary to research the stability and H∞control problem of uncertain systems with time delays. According to the known conclusions at the present, based on Lyapunov stability theory, combined with the freedom matrix and the approach of linear matrix inequality, this paper investigates the stability and H∞control problem of systems with time-delay.The main conclusions in this paper are as follows:(1) The problem of new stability criteria for uncertain neutral systems with state delay is studied. By choosing appropriate Lyapunov functions, using Leibniz-Newton, the adaptive enlargement of integral inequality and the approach of LMI, the new conditions of asymptotically stability for uncertain neutral systems are obtained. Finally, numerical examples are given to show the effectiveness of our results and much less conservative.(2) The H∞control problem for dynamic systems with state delay is concerned in this paper. Design a no memory state feedback controller to made the closed-loop system asymptotically stable and obtained the minimum value of the H∞perfor-mance index 7, when there is disturbance input w(t). At last, a numerical example is given to illustrate the feasibility of our results.(3) The problem of the H∞non-fragile observer-based control for dynamic systems with state delay is investigated. In practical controls, there are parameters in many controllers. Then the controllers exist high non-fragile. Based on the known conclusions, Lyapunov stability theory and LMI, the problem of this H∞non-fragile control is solved. Finally, numerical examples verify the feasibility and effectiveness of the conclusions.