Several Classes Of Differential Dynamic System With Non-fixed Time Impulsive Control

When applying pulse to system, we can not ensure that places pulse on the fixed time, just what we had originally planned to apply pulse at the moment t, but only in a small window of time(t-a,t +a) to discuss problems, which a is a small positive number. One important feature of the time-varying impulses is that both the destabilizing and stabilizing impulses exist in the model simultaneously. Generally,there are two kinds of impulsive dynamics system, unstable and stable pulse sequence,including unstable pulse sequence refers to inhibit the stability of dynamics system,pulse sequence stability means can enhance the stability of dynamics system. In this paper, we analyze uncertain Luré systems with impulse time window, the nonautonomous chaotic system with impulse time window and the coupled neural networks with time-varying impulses. Applying the impulsive control system with impulse time window, we can take advantage of constructing Lyapunov function,shrinking inequation, the comparison theorem and mathematical induction to prove its stability, it is no longer places pulse on the fixed time, but in a very small time window to apply, finally, we come to the conclusion. For the coupled neural networks with time-varying impulses, by using the method of constructing Lyapunov function, then apply the definition of global exponential stability to prove that the system stability,finally, we obtain the delayed coupled neural networks with time-varying impulses is said to be exponentially stable.The thesis is organized as follows:In chapter 1, we analyze that the stability of uncertain Luré systems with impulse time windows. By using comparison system, we get the terms of the stability of the impulsive control system, finally, the result is illustrated to be efficient through an example.In chapter 2, we research the practical stability of impulsive control and synchronization of nonautonomous chaotic system with impulsive time windows, Use mathematical induction to prove its stability, and finally illustrate theorem wasestablished.In chapter 3, we addresses the stability problem of coupled neural networks with time-varying impulses. we put the destabilizing and stabilizing impulses are taken into account, through controlling the time-varying impulsive strength, using the definition of exponential stability, we have the exponential stability of delayed coupled neural networks with time-varying impulses, finally, an example is given to demonstrate the effectiveness of the theoretical results.