Stability,Stabilization And Synchronization Control Of Several Classes Of Complex Dynamical Systems

Delays,impulsive phenomena,random phenomena and nonlinear situations exist inevitably in the real systems and the external environments,which influence the dynamical behavior of systems.To realistically describe the practical problem,and accurately reflect the dynamic characteristics of natural and social engineering systems,it often used in large systems or complex systems.Complex systems are widely used in engineering,neural network,ecology and control theory and other fields.Therefore,the stability and control theory of complex systems with nonlinear,time delay,impulsive,stochastic phenomena and other factors are the current research hotspots.This doctoral dissertation aims at the stability,stabilization and synchronization control for nonlinear impulsive neural networks,time delay stochastic systems,and network systems with diffusion terms.The main contributions of the dissertation are summarized as follows:1.The background,research significance and current situation of the selected topic are reviewed.An interesting exploration with the research method for the problem of time delay,impulse and synchronous control are introduced briefly.Some preliminaries are also presented.2.A class of Cohen-Grossberg neural networks with multiple proportional delays and impulsive are considered.Without assuming the boundedness and monotonicity of activation functions and boundedness of variable delays,we establish new sufficient conditions for global asymptotic stability and uniform asymptotic stability of the equilibrium point for multiple proportional delayed Cohen-Grossberg neural networks.These results generalize a few previous known results and remove some restrictions on the neural networks.Numerical example is provided to show that the proposed criteria are less conservative than some results in the literature.3.This chapter is concerned with the dissipativity and stability of the theoretical solutions of a class of nonlinear multiple time delay integro-differential equations.At first,we give a generalized the Halanay inequality which plays an important role in the study of dissipativity and stability of integro-differential equations.Then,we apply the generalized Halanay inequality to the dissipativity and the stability of delay integrodifferential equations and some interesting results are obtained.Finally,two examples are provided to demonstrated the effectiveness and advantage of the theoretical results.4.In this chapter,we investigate exponential synchronization of Cohen-Gross berg neural network with mixed time-varying delays and unknown parameters by stochastic analysis theory and general impulsive controller.A nonlinear impulsive controller and stochastic perturbation are designed to guarantee that the response system can be synchronized with a drive system by utilizing Lyapunov stability theory and analysis techniques.Finally,two numerical examples and its simulations are provided to demonstrated the effectiveness and advantage of the theoretical results.5.Mainly from the periodic intermittent adaptive feedback control,impulsive control to study reaction diffusion neural network,it makes the drive system and response system to achieve synchronization.By constructing Lyapunov function,the relevant theory of stability and the invariance principle of functional differential equations,the results are proved.Using the wirtinger’s inequality and the impulsive halanay inequality,the proof is simple.At last,an example is provided to demonstrated the effectiveness and advantage of the theoretical results.6.Based on combining graph theory with stochastic differential equation and Lyapunov method,new method are obtained and sufficient conditions on pth moment exponentially stable and almost surely exponentially stable for the multi-group coupled models with stochastic perturbations are provided.And we focuses on stabilization for multi-group coupled models stochastic by delay feedback control and nonlinear impulsive control.Some sufficient conditions are obtained about stabilization of the multi-group coupled stochastic models.At last,two examples are worked out to demonstrate the effectiveness and advantage of the theoretical results.Finally,the main results of the dissertation are concluded and some issues for future research are proposed.