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The asymptotic synchronization problem of chaotic Lur'e systems in the master-slave framework was explored in this paper. A time-varying delay feedback controller with quantization considerations and a delay-product-type Lyapunov-Krasovskii functional technique were employed to tackle this problem. Consider an error system based on master and slave systems, for which sufficient asymptotic stability requirements are developed to assure that the addressed system achieves proper synchronization. Following that, the desired control gain was determined by finding a feasible solution to these stability requirements. The results of this paper were validated using a numerical example with simulations, which revealed that they were superior to previously published ones. [ABSTRACT FROM AUTHOR]

The asymptotic synchronization problem of chaotic Lur'e systems in the master-slave framework was explored in this paper. A time-varying delay feedback controller with quantization considerations and a delay-product-type Lyapunov-Krasovskii functional technique were employed to tackle this problem. Consider an error system based on master and slave systems, for which sufficient asymptotic stability requirements are developed to assure that the addressed system achieves proper synchronization. Following that, the desired control gain was determined by finding a feasible solution to these stability requirements. The results of this paper were validated using a numerical example with simulations, which revealed that they were superior to previously published ones.

The robust synchronization of uncertain master–slave Lur'e systems based on time-delayed feedback control is further investigated. A less conservative synchronization stability criterion and a less conservative robust synchronization stability criterion than some recent published references are proposed via Lyapunov stability theory. First, an augmented delay-dependent Lyapunov–Krasovskii functional (LKF) is constructed, where some single integral terms are augmented to the integrand component of a single-integral subfunction. This not only increases some coupling information on some system variables but also increases the coupling information on some necessary variables contained in the inequality lemmas, which can make full use of the inequality lemmas and reduce the conservatism of the synchronization stability criterion. Second, to overcome the nonlinear phenomena in the synchronization criterion, the novel negative definite inequality equivalent transformation lemma is used to transform the nonlinear inequalities to the linear matrix inequalities (LMIs) equivalently, which can be easily solved by the MATLAB LMI-Toolbox. Finally, some common numerical examples are presented to show the effectiveness of the proposed approach. [ABSTRACT FROM AUTHOR]

This brief investigates the synchronization problem of chaotic Lur’e systems by employing sampled-data control. First of all, a new fragmentation approach is provided based on two partition coefficients, which can divide the sampling interval into four parts. Next, taking the fragmented states into account, a novel fragmentation looped-functional is constructed. Then, not only the fragmented states, but also the fragmented state system equations are utilized in the sufficient synchronization conditions. Moreover, according to the transformed free-matrix-based integral inequality (TFMBII) and Schur complement, the synchronization criterion is presented in the form of linear matrix inequalities (LMIs). Eventually, the effectiveness and superiority of the proposed criterion are illustrated through a benchmark numerical example. [ABSTRACT FROM AUTHOR]

This brief focus on the event-triggered synchronization of networked chaotic Lur’e systems. To relieve the burden of communication network with limited bandwidth, a novel memory-based event-triggered mechanism with the past information of the system is presented. The synchronization error system under the memory-based event-triggered mechanism is modeled by a distributed delay system. Applying an integral inequality based on Legendre polynomials, a novel synchronization condition is derived via linear matrix inequalities. Finally, a Chua’s circuit is adopted to illustrate the advantage of the proposed control strategy. [ABSTRACT FROM AUTHOR]

This paper proposes a new approach to investigate the problem of designing sampled-data controller for master–slave synchronization of chaotic Lur'e systems with time delay. Compared with existing methods, this method can make full use of the information of actual sampling pattern. To reflect more realistic the information on both the intervals e(t) to e (t k) and e(t) to e (t k + 1) , a novel two-side sampling-interval-dependent discontinuous Lyapunov functional (DLF) is constructed, which can fully utilizes the available characteristics of actual sampling information. Based on this DLF and by using modified free-matrix-based integral inequality, novel less conservative stability criteria of the synchronization error system are derived in the form of linear matrix inequalities, which guarantee the master system synchronizes with the slave system. At the same time, the gain matrix of the sampling controller is gained with a bigger sampling interval than the previous conclusions. Simulation results are provided to demonstrate the effectiveness and benefits of the presented synchronization scheme. [ABSTRACT FROM AUTHOR]

The master-slave synchronization (MSS) issue of chaotic Lur'e systems (LSs) with time-varying delay (TVD) is explored in this work by means of feedback control. After taking the nonlinear function into full consideration, a creative Lyapunov-Krasovskii functional (LKF) is attained. Then novel criteria which ensure the synchronization of the studied systems are obtained with the aid of the improved inequality technique and the reciprocally convex combination method to cope with the derivative of LKF. The effectiveness and virtues of the synchronization conditions are testified via the notable Chua's circuit in three different cases. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

This paper is concerned with the problem of sampled-data exponential synchronization for chaotic Lur'e systems (CLSs) in the form of master-slave framework. An improved time-dependent Lyapunov functional (TDLF) is put forward to fully exploit the accessible information about sampling characteristics and nonlinearities of the CLS. By resorting to the improved TDLF, a new synchronization criterion is established, which ensures the synchronization error system is globally exponentially stable. An illustrative example is offered to demonstrate the validity and virtue of the proposed design methodology.

• The extended Wirtinger-inequality-based Lyapunov approach is newly proposed. • A zero equality is formulated, which can capture the information of system at the dynamic partitioning point. • A quantized sampled-data controller is designed. • Compared with some existing results, less conservative synchronization criteria are established for chaotic Lur'e systems. We design a quantized sampled-data controller for synchronization of delayed chaotic Lur'e systems. A new approach, extended Wirtinger-inequality-based Lyapunov–Krasovskii functional, is firstly proposed. This approach grasps more sampling information by introducing more free matrices in comparison with some existing methods. Using the system information at the dynamic partitioning point, a zero equality is formulated to fully utilize the inner sampling information. Based on the new approach and zero equality, some novel synchronization criteria are established. In the meantime, the desired quantized sampled-data control gain is obtained with larger sampling period than those in the existing works. Finally, two numerical examples illustrate the merits of the method. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

Abstract This paper investigates the issue of sampled-data synchronization for a class of chaotic Lur'e systems (CLSs), where a novel sampling interval fragmentation approach (SIFA) is proposed. To this end, first, by partitioning sampling interval into several nonuniform segments based on a geometric series and taking advantage of the convex combination technique, a newly discontinuous Lyapunov–Krasovskii functional (LKF) is developed for the first time to analyze the synchronization problem of such systems, which significantly uses more information on actual sampling behavior of the system. Meanwhile, an uniform sampling interval fragmentation approach (USIFA) is also taken into account. Then, some relaxed sampled-data synchronization criteria of concerned systems are formulated in framework of matrix inequalities with a larger sampling period. Two numerical simulations are provided to demonstrate the superiority and effectiveness of the derived results. [ABSTRACT FROM AUTHOR]

This brief deals with the problem of master–slave synchronization for chaotic Lur’e systems with aperiodic sampled data. Specifically, a novel aperiodic adaptive event-triggered communication mechanism is introduced to reduce the transmission load, which covers the previous ones as special cases. By partially resorting to the time-dependent Lyapunov function, a new synchronization criterion is derived, which depends on both the upper and lower bounds of variable sampling interval. Finally, Chua’s circuit system is chosen as an illustrative example to show the virtue and effectiveness of the achieved synchronization strategies. [ABSTRACT FROM AUTHOR]

This paper investigates the problem of designing stochastic sampled-data controller for exponential synchronization of chaotic Lur’e systems (CLSs) via a new approach. Specially, first, multiple stochastic sampling intervals with given probabilities are considered and satisfy Bernoulli distribution. Second, unlike other studies, a unified probability framework, which takes sampling interval and time-varying delay into account, is proposed for the first time to design the controller. Based on this unified probability framework, an augmented Lyapunov–Krasovskii functional (LKF) with some new terms is constructed, which can take full advantage of the available information on actual sampling pattern. Different from some existing LKFs needing to be positive definite on the whole sampling intervals, by the new inequality in Lemma 1, the LKF is positive definite only requiring to be positive definite at sampling times. Third, less conservative synchronization criterion is derived and the desired stochastic sampled-data controller is designed. Finally, numerical simulations of Chua’s circuit and neural network are provided to show the effectiveness and advantages of the proposed results. [ABSTRACT FROM AUTHOR]

This paper investigates the exponential synchronization of chaotic Lur'e systems (CLSs) with time-varying communication delays through event-triggered sampling control. Specially, first, a discrete event-triggered sampling control scheme, which only sends necessary sampling signal through the network, is designed for CLSs. By using this controller, the number of control updates could greatly reduce. Second, by getting utmost out of the usable information on the actual sampling pattern, some new sawtooth structure terms are introduced in the constructed Lyapunov-Krasovskii functional (LKF). It is worth mentioning that, different from some existing results to restrict the LKF to be positive define on the whole sampling intervals, the LKF is positive definite only needing at sampling times thanks to the use of the new inequality in Lemma 1. Third, less conservative synchronization criteria are established and the desired control gain matrix is obtained. Finally, two Chua's circuit numerical simulations are presented to validate the feasibility and effectiveness of the theoretical results. [ABSTRACT FROM AUTHOR]

This paper studies the problem of exponential synchronisation of chaotic Lur'e systems (CLSs) via memory feedback proportional-integral-derivative (PID) control scheme. First, a novel augmented Lyapunov–Krasovskii functional (LKF) is constructed, which can make full use of the information on time delay and activation function. Second, improved synchronisation criteria are obtained by using new integral inequalities, which can provide much tighter bounds than what the existing integral inequalities can produce. In comparison with existing results, in which only proportional control or proportional derivative (PD) control is used, less conservative results are derived for CLSs by PID control. Third, the desired memory feedback controllers are designed in terms of the solution to linear matrix inequalities. Finally, numerical simulations of Chua's circuit and neural network are provided to show the effectiveness and advantages of the proposed results. [ABSTRACT FROM PUBLISHER]

The master-slave synchronization problem for a class of chaotic systems is investigated in this paper. It is assumed that quantized sampled measurement with constant delay is available for the controller, and event-triggered mechanism is introduced to decide whether the signal to be quantized should be transmitted. By taking the quantized synchronization error as control signal and constructing appropriate Lyapunov functional, a new sufficient condition for the networked synchronization of chaotic Lur'e systems with quantized feedback based on event-triggered mechanism is obtained. The master-slave synchronization of chaotic Chua's circuit system is simulated to demonstrate the efficiency of the proposed approach. The application to the secure communication is also investigated by using the chaotic nature of the unified attractors and the proposed synchronization mechanism. [ABSTRACT FROM AUTHOR]

This paper investigates the problem of sampled-data synchronization of chaotic Lur'e systems with time-varying sampling. A novel Lyapunov functional, which is continuous in time and makes full use of the available information about the sampling pattern, is constructed to synchronize the chaotic Lur'e systems. By using a free-weighting matrix approach and solving a set of linear matrix inequalities (LMIs), a sampled-data controller is obtained. The effectiveness and the validity of the proposed theoretical result are illustrated by two numerical examples. [ABSTRACT FROM AUTHOR]

This paper presents a predictive synchronization method for discrete-time chaotic Lur'e systems with input constraints by using time-varying delayed feedback control. Based on the model predictive control scheme, a delay-dependent stabilization criterion is derived for the synchronization of chaotic systems that is represented by Lur'e systems with input constraints. By constructing a suitable Lyapunov-Krasovskii functional and combining with a reciprocally convex combination technique, a delay-dependent stabilization condition for synchronization is obtained via linear matrix inequality (LMI) formulation. The control inputs are obtained by solving a min-max problem subject to cost monotonicity, which is expressed in terms of LMIs. The effectiveness of the proposed method will be verified throughout a numerical example. [ABSTRACT FROM AUTHOR]