Impulsive Synchronization Scheme Research Articles

Impulsive Synchronization of Fractional-Order Chaotic Systems With Actuator Saturation and Control Gain Error

This paper investigates the impulsive synchronization scheme of fractional-order chaotic systems with actuator saturation and control gain error. Based on the theory of fractional order system and impulsive differential system, discontinuous Lyapunov stability and matrix inequality approach, some new sufficient conditions are derived to guarantee the impulsive synchronization of a general class of fractional order chaotic systems. It is worth mentioning that the actuator saturation and control gain error are discussed simultaneously, which is more rigorous and practical in real systems. Finally, some simulation results verify the correctness and effectiveness of the theoretical results.

Adaptive impulsive synchronization for a class of fractional order complex chaotic systems

In this paper, a new lemma is proposed to study the stability of a fractional order complex chaotic system without dividing the complex number into real and imaginary parts. The proving process of the new lemma combines the fundamental properties of the complex field and the fractional order extension of the Lyapunov direct method. It extends the fractional order extension of the Lyapunov direct method from the real number field to the complex number field. Based on the new lemma, we propose a new impulsive synchronization scheme for fractional order complex chaotic systems. The numerical simulation results also show the validity of our conclusion.

Impulsive Stabilization and Impulsive Synchronization of Discrete-Time Delayed Neural Networks

This paper investigates the problems of impulsive stabilization and impulsive synchronization of discrete-time delayed neural networks (DDNNs). Two types of DDNNs with stabilizing impulses are studied. By introducing the time-varying Lyapunov functional to capture the dynamical characteristics of discrete-time impulsive delayed neural networks (DIDNNs) and by using a convex combination technique, new exponential stability criteria are derived in terms of linear matrix inequalities. The stability criteria for DIDNNs are independent of the size of time delay but rely on the lengths of impulsive intervals. With the newly obtained stability results, sufficient conditions on the existence of linear-state feedback impulsive controllers are derived. Moreover, a novel impulsive synchronization scheme for two identical DDNNs is proposed. The novel impulsive synchronization scheme allows synchronizing two identical DDNNs with unknown delays. Simulation results are given to validate the effectiveness of the proposed criteria of impulsive stabilization and impulsive synchronization of DDNNs. Finally, an application of the obtained impulsive synchronization result for two identical chaotic DDNNs to a secure communication scheme is presented.

Synchronization of a class of chaotic systems using small impulsive signal

In this paper the issue of impulsive synchronization of a class of uncertain chaotic systems with parameters perturbation is investigated. Applying the impulsive theory and linear matrix inequality technique, some less conservative and easily verified criteria for impulsive synchronization of chaotic systems are derived. The proposed impulsive synchronization scheme is applied to the chaotic Murali–Lakshmanan–Chua circuit and hyperchaotic Chen and the corresponding synchronization conditions are derived. Moreover, the boundaries of the stable region are also estimated according to the equidistant impulse interval. The effectiveness of the method is demonstrated by the computer simulation.

Intermittent Impulsive Synchronization of Hyperchaos with Application to Secure Communication

AbstractIn this paper, a hyperchaotic system is presented as the chaotic carrier to encrypt information in secure communication. The sensitivity to the system parameters and delay of the hyperchaotic system, i.e., its chaotic degree indicated by the number of positive Lyapunov exponents, increases with its system parameter and delay, guaranteeing a large enough key space when one selects its system parameter and delay as the secret key. Furthermore, we develop an intermittent impulsive synchronization scheme (IISS) to achieve chaos synchronization, a crucial process in chaos‐based secure communication. In our scheme, impulsive control is only activated in the control windows, not during the whole time, which breaks through the limitation on the upper bound of the impulsive intervals in the general impulsive synchronization scheme (GISS). Specifically, IISS improves the security of the chaos‐based secure communication scheme since the encrypted signal (cipher) is transmitted in the free windows, different from the synchronization signal in the control windows. Finally, a secure communication scheme employing our hyperchaotic system and IISS technique is proposed and numerical results are given to demonstrate the performance of this scheme.

A new impulsive synchronization of Chen hyper-chaotic system and Lü hyper-chaotic system

This work presents an impulsive synchronization scheme of the Chen hyper-chaotic system and Lü hyper-chaotic system with the assumption that all of the parameters are unknown. Sufficient conditions are derived, based on the impulsive differential stability theory, for achieving the impulsive synchronization with the desired scaling factor. By the adaptive control technique, the control laws and the corresponding parameter update laws are obtained such that the impulsive synchronization of the two non-identical hyper-chaotic systems can be realized. Simulation results also illustrate the effectiveness of the proposed control scheme.

Intermittent Impulsive Synchronization of Chaotic Delayed Neural Networks

In this paper, a novel intermittent impulsive synchronization scheme is proposed to realize synchronization of two chaotic delayed neural networks. Intermittent impulsive control breaks through the limitation of the upper bound of the impulsive intervals in general impulsive control. In our synchronization scheme, impulsive control is only activated in the control windows, rather than during the whole time. Several synchronization criteria for chaotic delayed neural networks are established utilizing the method of linear matrix inequalities (LMI) and the Lyapunov–Razumikhin technique. Two numerical examples are given to demonstrate the effectiveness of our main results.

An improved impulsive control approach to robust lag synchronization between two different chaotic systems

In this paper, a novel robust impulsive lag synchronization scheme for different chaotic systems with parametric uncertainties is proposed. Based on the theory of impulsive functional differential equations and a new differential inequality, some new and less conservative sufficient conditions are established to guarantee that the error dynamics can converge to a predetermined region. Finally, some numerical simulations for the Lorenz system and Chen system are given to demonstrate the effectiveness and feasibility of the proposed method. Compared with the existing results based on so-called dual-stage impulsive control, the derived results reduce the complexity of impulsive controller, moreover, a larger stable region can be obtained under the same parameters, which can be shown in the numerical simulations finally.

Robust Synchronization by Time-Varying Impulsive Control

This brief introduces a new impulsive synchronization scheme for a class of nonlinear systems with time-varying impulsive interval. Different from existing fixed time synchronization schemes, the impulsive synchronization intervals in our scheme are adaptive to the states of the driving system. Compared with existing schemes, the average impulsive interval can be enlarged significantly. Thus, the requirement of bandwidth for the transmission of impulsive signal is also reduced.

Nonlinear observer-based impulsive synchronization in chaotic systems with multiple attractors

The issue of impulsive synchronization of the coupled Newton–Leipnik system is investigated. Based on the impulsive stability theory, nonlinear observer-based impulsive synchronization scheme is derived. A new and less conservative criteria for impulsive synchronization via nonlinear observer is proposed. The boundary of the stable regions is also estimated. One important advantage of the proposed method is that it is also applicable for the systems with more than one attractor. Numerical simulations on Newton–Leipnik system are illustrated to verify the theoretical results.

Robust lag synchronization between two different chaotic systems via dual-stage impulsive control

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.

Some new less conservative criteria for impulsive synchronization of a hyperchaotic Lorenz system based on small impulsive signals

In this Letter the issue of impulsive Synchronization of a hyperchaotic Lorenz system is developed. We propose an impulsive synchronization scheme of the hyperchaotic Lorenz system including chaotic systems. Some new and sufficient conditions on varying impulsive distances are established in order to guarantee the synchronizability of the systems using the synchronization method. In particular, some simple conditions are derived for synchronizing the systems by equal impulsive distances. The boundaries of the stable regions are also estimated. Simulation results show the proposed synchronization method to be effective.

A practical approach to robust impulsive lag synchronization between different chaotic systems

In this paper, a practical impulsive lag synchronization scheme for different chaotic systems with parametric uncertainties is proposed. By virtue of the new definition of synchronization and the theory of impulsive differential equations, some new and less conservative sufficient conditions are established to guarantee that the error dynamics can converge to a predetermined level. The idea and approach developed in this paper can provide a more practical framework for the synchronization between identical and different chaotic systems in parameter perturbation circumstances. Simulation results finally demonstrate the effectiveness of the method.

Impulsive synchronization of chaotic Lur'e systems via partial states

In this Letter, the problem of impulsive synchronization of two identical Lur'e systems via partial states is studied. The problem arises in the situation when only partial states of the driven systems are available. By using the method of the variation of parameters for linear impulsive systems and some analysis technique, a sufficient condition for the existence of the impulsive control law for synchronization via partial states is derived. The sufficient condition is given in terms of linear matrix inequalities concerning the interconnection matrices. By using this result, we propose a new impulsive synchronization scheme for a class of Lur'e systems. The new impulsive synchronization scheme only exerts the impulsive input on partial states of the driven system and is characterized by a set of conditions related to the impulsive interval bound, the impulsive magnitude and a coupling condition between them. The proposed impulsive synchronization method is illustrated through Chua's circuit.

Uniform stability of discrete impulsive systems

This article studies discrete impulsive systems. The uniform stability (uniformly asymptotic stability and quasi-exponential stability) criteria are established for linear discrete impulsive system and a class of nonlinear discrete impulsive systems, respectively. These stability criteria are expressed in terms of fairly simple algebraic conditions so that they are easy to be tested. Moreover, by using the stability criteria, a discrete impulsive synchronization scheme is designed to synchronize two discrete chaotic systems. Finally, some examples are given to illustrate results obtained by us.

Robust Impulsive Synchronization for a Class of Unified Chaotic Systems with Parameter Uncertainty

For a class of unified chaotic systems with parameter uncertainty, a robust impulsive synchronization scheme is proposed. Based on the theory of impulsive differential equations, some new and less conservative sufficient conditions are established in order to guarantee the robust synchronization of the chaotic systems. In particular, some simple and practical conditions are derived in synchronizing the chaotic systems by equal impulsive distances and control gains. Simulation results finally demonstrate the effectiveness of the method.

Impulsive Synchronization of Lü Chaotic System Based on Small Impulsive Signal

In this Letter the issue of impulsive synchronization of the Lu chaotic system is developed. We propose an impulsive synchronization scheme of the Lu chaotic system including chaotic systems. Some new and sufficient conditions on varying impulsive distance are established in order to guarantee the synchronizability of the systems using the synchronization method. In particular, some simple conditions are derived in synchronizing the systems by equal impulsive distances. The proposed impulsive synchronization scheme is applied to the Lu chaotic system and the numerical example demonstrates the effectiveness of the method. The boundaries of the stable regions are also estimated.

Practical impulsive synchronization of chaotic systems with parametric uncertainty and mismatch

Recently, there has been increasing interest in the synchronization of two chaotic systems and some significant results have been reported. In these results, a strong assumption that the two chaotic systems should be identical, i.e., without any mismatch, is imposed. Furthermore, system parameters are also assumed known exactly. Clearly, these are impractical. In this Letter, pure impulsive synchronization is considered. We quantitatively establish a relationship between a pre-specified bound of the synchronization error and the length of impulsive intervals in the presence of both parametric uncertainties and mismatch between the two systems. This is the first available result in the area, to the knowledge of the authors. With such a relationship as a guideline to choose impulsive intervals, a practical impulsive synchronization scheme is obtained. With the proposed scheme, the magnitude of the synchronization error is theoretically ensured to approach to and stay within the pre-specified bound which can be arbitrarily small. Simulation studies on the Lorenz system also verify the effectiveness of the proposed scheme.

EXPERIMENTAL INVESTIGATION OF IMPULSIVE SYNCHRONIZATION BETWEEN TWO MIXED-MODE CHAOTIC CIRCUITS

This study presents an experimental investigation of impulsive synchronization between two Mixed-mode chaotic circuits. The proposed impulsive synchronization scheme has been tested by applying a switching process with frequency range from 500 Hz to 1 MHz. Experimental results recorded with a digital storage oscilloscope revealed that the proposed scheme can be impulsively synchronized with good quality for switching frequencies higher than 10 kHz.

Impulsive synchronization for Takagi–Sugeno fuzzy model and its application to continuous chaotic system

Recently, chaos synchronization based on T–S fuzzy model has attracted much attention because of the applicability in the case of uncertainty. In the fuzzy control scheme, linear and adaptive control methods have been introduced to solve the control problem. In this Letter, an impulsive synchronization scheme for T–S fuzzy model is developed. The proposed impulsive control scheme seems to have a simple control structure and may need less control energy than the normal continuous ones for the synchronization of T–S fuzzy system. Sufficient conditions for the impulsive synchronization are derived. The method is illustrated by applications to continuous chaotic systems and the simulation results demonstrate the effectiveness of the proposed control method.