Synchronization Of Chaotic Lur Research Articles

Further results on synchronization of chaotic Lur’e systems based on aperiodic time-triggered intermittent control

Aperiodic time-triggered intermittent control (ATIC) is presented to investigate the exponential synchronization issue of chaotic Lur’e systems (CLSs). In our work, for CLSs, the mathematical expression of ATIC is put forward initially. Different from time-triggered intermittent control (TIC), ATIC allows aperiodic sampling. The aperiodic sampling characteristic of ATIC makes it more flexible and adaptable in complex environments, which greatly increases its applications. Then, for the deduced ATIC error system, a key lemma is established, which demonstrates that, on control or free time intervals, the bound of the error vector norm at any instance can be described by the multiple of its norm at initial instance. Further, based on the lemma and a mixed time-dependent Lyapunov functional (MTLF), the exponential stability theorem is given for the deduced ATIC error system. Consequently, the exponential synchronization criterion with less conservativeness is obtained for CLSs via ATIC. With its aid, the design method of ATIC is proposed. Finally, the validity and superiority of ATIC are verified by a simulation example.

Synchronization of chaotic Lur’e systems with time-delays via quantized output feedback control

In this paper, the asymptotic stability for chaotic Lur’e systems (CLSs) is studied. A new control method, which involves both state quantizer and control quantizer, is presented. In addition, dynamic parameters of quantizers and controller are designed synchronously to ensure the asymptotic synchronization of the master–slave systems. Moreover, by solving linear matrix inequalities, the corresponding dynamic parameters and control gain can be given. Finally, one numerical simulation and two practical simulations are raised to prove the effectiveness of the control strategy.

Asymptotic Stability of Master-slave Systems Using Sampled-data Controller with Time-delay

In this paper, the synchronization of Chaotic Lur’e systems subject to aperiodic sampling is investigated. It is shown that sampling interval is bounded and nonuniform. A modified free-matrix-based (MFMB) time-dependent Lyapunov functional is developed to capture the information on sampling pattern, which is sufficiently used to analyze stability of Chaotic Lur’e systems. For a special case that the sampled-data controller suffers constant input delay, a discontinuous Lyapunov functional is presented based on the vector extension of Wirtinger’s inequality. The obtained stability condition leads to a less computational complexity than some of existing works. A longer value on the calculation of sampling interval is achieved. Two illustrative examples demonstrate the effectiveness of designed methods and less conservatism of the obtained results.

Synchronization of chaotic Lur’e systems with state and transmission line time delay: a linear matrix inequality approach

This paper is concerned with the problem of the master–slave synchronization of chaotic Lur’e systems with multiple time delays in their states and transmission line. Based on the Lyapunov–Krasovskii functional, some delay-dependent synchronization criteria are obtained and formulated in the form of linear matrix inequalities (LMIs) to ascertain the global asymptotic stability of the error system such that the slave system is synchronized with the master. With the help of the LMI solvers, the time-delay feedback control law can easily be obtained. The effectiveness of the proposed method is illustrated using some numerical simulations performed on two chaotic systems.

Networked Reliable Synchronization of Chaotic Lur’e Systems with Sector- and Slope-Restricted Nonlinearities

This paper investigates the networked reliable synchronization problem of chaotic Lur'e systems containing the sector- and slope-restricted nonlinearities. The reliable synchronization of chaotic Lur'e systems is achieved based on networked control techniques. Moreover, some sufficient conditions are obtained and these conditions depend on various network-related parameters, fault indicating matrices, sector and slope bounds. Finally, a numerical example is provided to illustrate the validity of the proposed method.

Dissipative lag synchronization of chaotic Lur'e systems with unknown disturbances

This paper is concerned with the problem of dissipative lag synchronization (LS) for two identical Lur'e systems with unknown external disturbances. The disturbances are supposed to be generated by the exogenous systems with and without time-delay. Based on the disturbance-observer-based control method, the linear matrix inequality technique and the dissipativity theory, the disturbance observers are developed to ensure the boundedness of the disturbance error dynamics and the dissipativity of the resultant LS error system. By using the sliding-mode control (SMC) approach, an integral-type sliding surface function is constructed and a dissipative SMC law is established to render the disturbance rejection and realize LS between the master and slave systems, and an integral sliding-mode controller is designed to guarantee the reachability of the specified sliding surface. Finally, the Chua's circuit is used as a numerical example to illustrate the effectiveness of the proposed method.

Sampled-Data $$H_{\infty }$$ H ∞ Synchronization of Chaotic Lur’e Systems with Time Delay

This paper deals with the problem of robust $$H_{\infty }$$ synchronization of chaotic Lur’e systems with time-varying delays via sampled-data control. In order to make full use of the information about sampling intervals, nonlinear functions and time-varying delays, an improved Lyapunov–Krasovskii (L–K) functional is introduced. Based on reciprocal convex combination technique, sufficient conditions are derived in terms of linear matrix inequalities (LMIs) to ensure the asymptotic synchronization of the considered Lur’e system with a guaranteed $$H_{\infty }$$ performance. By solving the obtained LMIs, the required sampled-data control gain matrix is obtained, which assures the asymptotic stability of the error system and reduces the effect of external disturbance according to $$H_{\infty }$$ norm. Finally, the effectiveness and less conservatism of the proposed method are verified through numerical simulations of the Chua’s circuit and neural networks.

Sampled-Data Synchronization of Chaotic Lur’e Systems with Stochastic Sampling

In this paper, we study the problem of master---slave synchronization for chaotic Lur'e systems with sampled-data control. The sampling intervals are assumed to satisfy a Bernoulli distributed white noise sequence with fixed and given occurrence probability. By applying an input-delay approach, the probabilistic sampling system is transformed into a continuous time-delay system with stochastic parameters in the system matrices. Based on Lyapunov functional approach, a sufficient condition of exponentially mean-square synchronization is obtained by analyzing the corresponding synchronization error systems. The controller gains are designed by solving a set of linear matrix inequalities. Finally, two numerical examples are given to demonstrate the effectiveness of the proposed method.

Synchronization of chaotic Lur'e systems with time delays using sampled-data control.

The asymptotical synchronization problem is investigated for two identical chaotic Lur'e systems with time delays. The sampled-data control method is employed for the system design. A new synchronization condition is proposed in the form of linear matrix inequalities. The error system is shown to be asymptotically stable with the constructed new piecewise differentiable Lyapunov-Krasovskii functional (LKF). Different from the existing work, the new LKF makes full use of the information in the nonlinear part of the system. The obtained stability condition is less conservative than some of the existing ones. A longer sampling period is achieved with the new method. The numerical examples are given and the simulations are performed on Chua's circuit. The results show the superiorities and effectiveness of the proposed control method.

Synchronization of chaotic Lur’e systems with quantized sampled-data controller

In this paper, we consider the master–slave synchronization problem of chaotic Lur’e systems. It is assumed that only quantized sampled measurements are available for the controller. By modeling the synchronization error system as an input-delay system and constructing a new Lyapunov functional, a new sufficient condition and feedback controller design method for global exponential asymptotical synchronization of master and slave system are obtained. The proposed approach has taken the feature of sample-induced delay into consideration and simulation results show the less conservativeness.

Secure Communication via Synchronization of Lur’e Systems Using Sampled-Data Controller

In this paper, synchronization of chaotic Lur’e systems using sampled-data control is applied to the secure communication problem. The message is transmitted and masked by the techniques of n-cipher and a public key obtained by the chaotic Lur’e system. The decryption of the transmitted encrypted message to recover the original message at the receiver can be achieved by synchronizing the transmitter and receiver chaotic systems. Sampled-data feedback control is used for synchronization, and a sufficient condition for obtaining feedback gain is derived in terms of linear matrix inequalities using a discontinuous Lyapunov functional. The secure communication system is simulated via Matlab along with the Chua system to show the effectiveness of the proposed result.

Synchronization of chaotic Lur'e systems with delayed feedback control using deadzone nonlinearity

In this paper we present a synchronization method for chaotic Lur'e systems by constructing a new piecewise Lyapunov function. Using a delayed feedback control scheme, a delay-dependent stability criterion is derived for the synchronization of chaotic systems that are represented by Lur'e systems with deadzone nonlinearity. Based on the Lyapunov—Krasovskii functional and by using some properties of the nonlinearity, a new delay-dependent stabilization condition for synchronization is obtained via linear matrix inequality (LMI) formulation. The criterion is less conservative than existing ones, and it will be verified through a numerical example.

Synchronization for chaotic Lur’e systems with sector-restricted nonlinearities via delayed feedback control

In this paper, the effects of time delay on chaotic master–slave synchronization scheme are considered. Using delayed feedback control scheme, a delay-dependent stability criterion is derived for the synchronization of chaotic systems that are represented by Lur’e system with sector-restricted nonlinearities. The derived criterion is a sufficient condition for absolute stability of error dynamics between the master and the slave system. Using a convex representation of the nonlinearity, the stability condition based on the Lyapunov–Krasovskii functional is obtained via LMI formulation. The proposed delay-dependent synchronization criterion is less conservative than the existing ones. The effectiveness of our work is verified through numerical examples.

Adaptive Stabilization and Synchronization for Chaotic Lur'e Systems With Time-Varying Delay

In this paper, we propose an adaptive scheme for the stabilization and synchronization of chaotic Lur'e systems with time-varying delay. Based on the invariant principle of functional differential equations, the strength of the feedback controller is enhanced adaptively to stabilize and synchronize chaotic Lur'e systems. The derivative-constraint that the time-varying delay is required to be differentiable and its derivation is less than one can be removed by using LaSalle-Razumikhin-type theorems. The time-varying delay is allowed to be bounded without any additional constraint or unbounded with derivative-constraint. This method is analytical, rigorous and simple to implement in practice. In addition, it is quite robust against the effect of parameters uncertainty and noise. Two examples are provided to show the effectiveness of the proposed scheme. The results of the paper demonstrate the fruitfulness of the modern feedback and adaptive control theory application to the stabilization and synchronization problems for delayed chaotic systems.

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.

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.