Dynamical Behaviors And Impulsive Control Of Diferential Systems With Proportional Delay

In this master paper,the oscillation and global stability of differential systems with proportional delay are investigated,and moreover,the impulsive stabilization problem is also discussed for a class of nonlinear differential systems with proportional delay.This paper includes five chapters:As an introduction,the first chapter introduces the research purpose and significance of our work.Here the current research status are also presented.In the second chapter,we study the oscillation of the following differential equation with proportional delay(?)Some sufficient and necessary conditions of all for the equation are established for the oscillation of every solution of this equation.Furthermore,some explicit sufficient conditions are obtained.The third chapter discusses the stability of the following cellular neural networks with proportional delay(?)By employing Lyapunov method and LMI technique,sufficient conditions are obtained to guarantee the global power stable of the equilibrium point of the system.The result improves some relative results in the literature.Some examples and their simulations are given to illustrate the effectiveness of our results.In the fourth chapter,we investigate the stability of the following nonlinear differential systems with impulses and proportional delay(?)By employing the Lyapunov functions method and some improved Razumikhin technique,a new delay-dependent result is established to ensure that the zero solution of this addressed systems can achieve the global stability.Some impulsive control laws can be constructed to stabilize such system even if it is unstable.Some numerical examples along with their simulations are provided to demonstrate the feasibility of the obtained results.Chapter five summarizes our research results and presents some next works.