Lag Synchronization Scheme Research Articles

Projective–lag synchronization scheme between two different discrete-time chaotic systems

This paper addresses theoretical analysis of projective–lag synchronization between two different discrete-time chaotic systems. We overcome some limitations of previous works where projective–lag synchronization can only be achieved in continuous-time chaotic systems. In this paper, we realize projective–lag synchronization in discrete-time chaotic systems with the same order. Based on the Lyapunov stability theory and a nonlinear control scheme, the controllers are designed by using the relevant variables of master and slave systems, and we find sufficient conditions for the stability of the error dynamics. The correctness of theoretical analysis is verified by 2D and 3D discrete-time chaotic systems, respectively.

Finite-Time Lag Synchronization for Memristive Mixed Delays Neural Networks with Parameter Mismatch

This paper is devoted to study the finite time lag synchronization problem of memristive mixed delays neural networks with switching jumps and parameter mismatch. The main objective of this paper is to design simple linear feedback control such as the drive response systems can realize synchronization in the finite time. Several theoretical aspects are addressed, mean Filippov differential inclusion and set-valued map. Based on the Gronwall’s inequality and properties of differential operation, a new finite time lag synchronization scheme is proposed to guarantee that coupled memristive mixed delays neural networks are in a state of lag synchronization in finite time. In addition, finite lag synchronization criteria of two identical memristive mixed delays neural networks are also considered. Finally, numerical examples are presented to illustrate the effectiveness of the our proposed theorems.

Output-Feedback Controller Based Projective Lag-Synchronization of Uncertain Chaotic Systems in the Presence of Input Nonlinearities

This paper solves the problem of projective lag-synchronization based on output-feedback control for chaotic drive-response systems with input dead-zone and sector nonlinearities. This class of the drive-response systems is assumed in Brunovsky form but with unavailable states and unknown dynamics. To effectively deal with both dead-zone and sector nonlinearities, the proposed controller is designed in a variable-structure framework. To online learn the uncertain dynamics, adaptive fuzzy systems are used. And to estimate the unavailable states, a simple synchronization error is constructed. To prove the stability of the overall closed-loop system (controller, observer, and drive-response system) and to design the adaptation laws, a Lyapunov theory and strictly positive real (SPR) approach are exploited. Finally, three academic examples are given to show the effectiveness of this proposed lag-synchronization scheme.

Simple adaptive output-feedback lag-synchronization of multiple time-delayed chaotic systems

In this letter, a simple adaptive output-feedback controller is designed for lag-synchronization of two multiple time-delayed chaotic systems in the presence of uncertainty, external disturbances, and input nonlinearity. Based on Lyapunov stability theorem and adaptive techniques, sufficient conditions for lag-synchronization of these two systems are achieved. To deal with the existence of unknown time-delays in the system dynamics, the novel Lyapunov-Krasovskii functionals are used. Finally, a numerical simulation is presented to show the effectiveness of the proposed chaos lag-synchronization scheme.

$\mathcal{H}_{\infty}$ LAG SYNCHRONIZATION FOR CHAOTIC SYSTEMS

In this paper, we propose a new [Formula: see text] lag synchronization scheme for a general class of chaotic systems with external disturbance. Based on Lyapunov theory and linear matrix inequality (LMI) approach, the [Formula: see text] lag synchronization controller is presented to not only guarantee exponential lag synchronization but also reduce the effect of external disturbance to an [Formula: see text] norm constraint. The proposed controller can be obtained by solving a convex optimization problem represented by the LMI. As an application of the proposed method, the [Formula: see text] lag synchronization problem for Genesio–Tesi system is investigated.

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 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.

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.

Projective-Lag Synchronization of Coupled Multidelay Feedback Systems

In this study, we investigate the projective-lag synchronization model of coupled multidelay feedback systems. The master synchronizes with the slave under the lag synchronization scheme and there is a scale factor between the amplitudes of state variables. The driving signal is constituted by the sum of multiple nonlinear transformations of a delayed state variable. A sufficient condition for synchronization is considered under the Krasovskii–Lyapunov theory. The effectiveness of the proposed model is demonstrated and verified by examining specific examples using modified Mackey-Glass and Ikeda systems.

Some new criteria for lag synchronization of chaotic Lur'e systems by replacing variables control

Some new criteria for the chaotic lag synchronization are proposed. At first,lag synchronization scheme for identical master-slave Lur‘ e systems by replacing variables control and the relevant error system are given, and the relations between absolute stability of the error system and the chaotic lag synchronization are described. Then, based on a quadratic Lyapunov function, two new Lur‘ e criteria for the above chaotic lag synchronization are proved. Four corresponding frequency domain criteria are further derived by means of Meyer-Kalman-Yacubovia Lemma. These frequency domain criteria are applied to analyze the lag synchronization of general master-slave Chua's circuits so that some ranges of the parameters in which the master-slave Chua's circuits achieve chaotic lag synchronization by replacing single-variable control are attained. Finally, some examples are given to verify the theoretical results.

Lag synchronization of Rossler system and Chua circuit via a scalar signal

In this Letter, a chaotic lag synchronization scheme is proposed based on combining a nonlinear with lag-in-time observer design. Our approach leads to a systematic methodology, which guarantees the synchronization of a wide class of chaotic systems via a scalar signal. The proposed technique has been applied to synchronize two well-known chaotic systems: Rossler's system and Chua circuit.

Lag synchronization of hyperchaos with application to secure communications

In this paper, hyperchaotic lag synchronization is restated as a nonlinear and lag-in-time observer design issue. This approach leads to a systematic tool, which guarantees the lag synchronization of a wide class of chaotic or hyperchaotic systems via a scalar signal. By exploiting this result, we propose a hyperchaos-based cryptosystem scheme that combines the conventional cryptographic methods and the lag synchronization of chaotic circuits. The computer simulation results show that the lag synchronization scheme and the cryptosystem proposed in this paper are both feasible.