In this paper, a Takagi-Sugeno (T-S) fuzzy model-based method is proposed to deal with the problem of synchronization of two identical or different hyperchaotic systems. The T-S fuzzy models with a small number of fuzzy IF-THEN rules are employed to represent many typical hyperchaotic systems exactly. The benefit of employing the T-S fuzzy models lies in mathematical simplicity of analysis. Based on the T-S fuzzy hyperchaotic models, two fuzzy controllers are designed via parallel distributed compensation (PDC) and exact linearization (EL) techniques to synchronize two identical hyperchaotic systems with uncertain parameters and two different hyperchaotic systems, respectively. The sufficient conditions for the robust synchronization of two identical hyperchaotic systems with uncertain parameters and the asymptotic synchronization of two different hyperchaotic systems are derived by applying the Lyapunov stability theory. This method is a universal one of synchronizing two identical or different hyperchaotic systems. Numerical examples are given to demonstrate the validity of the proposed fuzzy model and hyperchaotic synchronization scheme.
This paper is devoted to investigating the scheme of exponential synchronization for uncertain stochastic impulsive perturbed chaotic Lur'e systems. The parametric uncertainty is assumed to be norm bounded. Based on the Lyapunov function method, time-varying delay feedback control technique and a modified Halanay inequality for stochastic differential equations, several sufficient conditions are presented to guarantee the exponential synchronization in mean square between two identical uncertain chaotic Lur'e systems with stochastic and impulsive perturbations. These conditions are expressed in terms of linear matrix inequalities (LMIs), which can easily be checked by utilizing the numerically efficient Matlab LMI toolbox. It is worth pointing out that the approach developed in this paper can provide a more general framework for the synchronization of multi-perturbation chaotic Lur'e systems, which reflects a more realistic dynamics. Finally, a numerical example is provided to demonstrate the effectiveness of the proposed method.
In this paper,the global impulsive exponential synchronization problem of a class of chaotic delayed neural networks(DNNs) with stochastic perturbation is studied.Based on the Lyapunov stability theory,stochastic analysis approach and an efficient impulsive delay differential inequality,some new exponential synchronization criteria expressed in the form of the linear matrix inequality(LMI) are derived.The designed impulsive controller not only can globally exponentially stabilize the error dynamics in mean square,but also can control the exponential synchronization rate.Furthermore,to estimate the stable region of the synchronization error dynamics,a novel optimization control algorithm is proposed,which can deal with the minimum problem with two nonlinear terms coexisting in LMIs effectively.Simulation results finally demonstrate the effectiveness of the proposed method.
In this paper,an improved impulsive lag synchronization scheme for different chaotic systems with parametric uncertainties is proposed.Based on the new definition of synchronization with error bound and a novel impulsive control scheme(the so-called dual-stage impulsive control),some new and less conservative sufficient conditions are established to guarantee that the error dynamics can converge to a predetermined level,which is more reasonable and rigorous than the existing results.In particular,some simpler and more convenient conditions are derived by taking the same impulsive distances and control gains.Finally,some numerical simulations for the Lorenz system and the Chen system are given to demonstrate the effectiveness and feasibility of the proposed method.
This paper aims to present some delay-dependent global asymptotic stability criteria for recurrent neural networks with time varying delays. The obtained results have no restriction on the magnitude of derivative of time varying delay, and can be easily checked due to the form of linear matrix inequality. By comparison with some previous results, the obtained results are less conservative. A numerical example is utilized to demonstrate the effectiveness of the obtained results.
This paper is concerned with the global asymptotic stability of a class of recurrent neural networks with interval time-varying delay. By constructing a suitable Lyapunov functional, a new criterion is established to ensure the global asymptotic stability of the concerned neural networks, which can be expressed in the form of linear matrix inequality and independent of the size of derivative of time varying delay. Two numerical examples show the effectiveness of the obtained results.
