Research On Finite-Time Synchronization Control Of Impulsive Chaotic Systems With Time-Varying Delays

Impulsive chaotic systems with time-varying delay take chaos,impulse jump and delay into consideration,which have attracted extensive attention from many scholars at home and abroad.In addition,most of the researches on the synchronization of impulsive chaotic systems focus on Lyapunov asymptotic synchronization in infinite time.However,in some work time is short of the actual system,it is not enough to consider the Lyapunov asymptotic synchronization,usually also need to pay attention to the coupling system transient performance,finite-time synchronization will reflect the transient performance of the system,so the finite-time synchronization of impulsive chaotic systems research has important practical significance.In this paper,the finite-time synchronization and control of impulsive chaotic systems with time-varying delays are studied.The main tasks are as follows:1.The finite-time synchronization problem of impulsive chaotic systems with time-varying delay is discussed by state feedback controller.Firstly,both desynchronizing impulse and synchronizing impulse are considered in the system model,and a finite-time synchronization criterion based on Lyapunov function method is established.Secondly,by constructing the appropriate Lyapunov-Krasovskii functional(L-K functional)and the average impulsive interval technique,the theoretical results of the system's finite-time synchronization are derived;Finally,two numerical examples are used to verify the feasibility of the proposed method.2.Considering the influence of uncertain parameters on impulsive chaotic systems,the finite-time synchronization problem for impulsive chaotic systems with uncertain time-varying delays is studied.For L-K functional derivative estimation,improved Bessel-Legendre inequality and free weight matrix methods are used for scaling,an appropriate state feedback controller is designed to realize the finite-time synchronization of driving-response system and the theoretical criterion of LMIs is obtained.Finally,a numerical example is given to demonstrate the effectiveness of the proposed method.3.Considering the influence of H_? control theory on the suppression of external interference,the finite-time synchronization and H_??control of impulsive chaotic systems with time-varying delays are studied.Firstly,a state feedback controller is designed and triple integral terms are added into the L-K functional.The integral terms in the functional derivatives are scaled down by using the auxiliary function integral inequality and inverse convex matrix inequality;Secondly,Based on H_??control theory and average impulsive interval method,the sufficient condition of finite-time synchronization of the system is given in the form of LMIs and the criterion to ensure that the system satisfies certain H_??performance index is given;Finally,the validity of the theoretical results is verified by simulation.