Impulse Control Method Of Time Delay System

There are many natural processes and system will undergo an instantaneous action which is not controlled by system or have a rapidly change in the state in short time,but this short disturbance is negligible when it compared with the time evolution of the system.If they are dealt with using pure continuous or pure discrete systems,it will lead to wrong result.The impulsive control systems can be used as an appropriate description of this kind of systems.The advantage of impulse control is using a small control pulse to control the system.In this paper,we mainly focus on the impulsive control of the time delay system,the main work is given as follows:1.The stability of a tumor growth model with time delay and impulse chemotherapy is analyzed.The globally stable condition for the periodic oscillation of the system under impulsive chemotherapy is derived.The boundedness of the solution is testified,and the permanence of the solution of the model is testified using Lyapunov function and comparnson theorem.Finally,we provide the simulation result for verifying the theorem.2.We investigate feedback impulse chemotherapy of tumor growth model wit,time delay.Firstly,we testify the permanence of the solution of the model under feedback impulse chemotherapy.Next,we give the condition which makes the tumor cells eliminate and preserve the immune cells.Finally,stimulation results are given to show that the condition is correct.3.We study the impulsive control and synchronization issues of the Chen system with direct time delay feedback,and apply it into communication systems.Firstly,we deduced the stability condition of impulsive control and synchronization of the impulsive time delay system.basing on the stability theory of impulsive delay differential equations.Secondly,we implement chaotic control and synchronization using the sufficient condition.Thirdly,combing both conventional cryptographic method and impulsive synchronization of chaotic Chen system with direct delay,we propose a new chaotic secure communication scheme.Finally,through the numerical and circuit stimulation results.we show the condition derived is correct.