Conservative Synchronization Criteria Research Articles

Free-matrix-based time-dependent discontinuous Lyapunov functional for synchronization of delayed neural networks with sampled-data control**Project supported by the National Natural Science Foundation of China (Grant No. 61304064), the Scientific Research Fund of Hunan Provincial Education Department, China (Grant Nos. 15B067 and 16C0475), and a Discovering Grant from Australian Research Council.

This paper is concerned with the synchronization of delayed neural networks via sampled-data control. A new technique, namely, the free-matrix-based time-dependent discontinuous Lyapunov functional approach, is adopted in constructing the Lyapunov functional, which takes advantage of the sampling characteristic of sawtooth input delay. Based on this discontinuous Lyapunov functional, some less conservative synchronization criteria are established to ensure that the slave system is synchronous with the master system. The desired sampled-data controller can be obtained through the use of the linear matrix inequality (LMI) technique. Finally, two numerical examples are provided to demonstrate the effectiveness and the improvements of the proposed methods.

Exponential synchronization of a class of neural networks with sampled-data control

This paper investigates the problem of the master-slave synchronization for a class of neural networks with discrete and distributed delays under sampled-data control. By introducing some new terms, a novel piecewise time-dependent Lyapunov-Krasovskii functional (LKF) is constructed to fully capture the available characteristics of real sampling information and nonlinear function vector of the system. Based on the LKF and Wirtinger-based inequality, less conservative synchronization criteria are obtained to guarantee the exponential stability of the error system, and then the slave system is synchronized with the master system. The designed sampled-data controller can be obtained by solving a set of linear matrix inequalities (LMIs), which depend on the maximum sampling period and the decay rate. The criteria are less conservative than the ones obtained in the existing works. A numerical example is presented to illustrate the effectiveness and merits of the proposed method.

Novel master–slave synchronization criteria of chaotic Lur’e systems with time delays using sampled-data control

This paper investigates the problem of master–slave synchronization of chaotic Lur’e systems (CLSs) with time delays by sampled-data control. First, a novel Lyapunov–Krasovskii functional (LKF) is constructed with some new augmented terms, which can fully capture the system characteristics and the available information on the actual sampling pattern. In comparison with existing results, the constraint condition of the positive definition of the LKF is more relax, since it is positive definite only requiring at sampling instants. Second, based on the LKF, a less conservative synchronization criterion is established. Third, the desired estimator gain can be designed in terms of the solution to linear matrix inequalities (LMIs). The obtained conditions ensure the master–slave synchronization of CLSs under a longer sampling period than remarkable existing works. Finally, three numerical simulations of Chua’s circuit and neural network are provided to show the effectiveness and advantages of the proposed results.

Pinning cluster synchronization of delayed complex dynamical networks with nonidentical nodes and impulsive effects

This paper studies the exponential cluster synchronization problem of complex dynamical networks with delayed couplings and nonidentical nodes. A new type of pinning impulsive control approach is proposed to achieve the exponential cluster synchronization of the considered network. By employing a time-dependent Lyapunov functional, less conservative cluster synchronization criteria are established in the form of linear matrix inequalities. Compared with the existing works, the constructed Lyapunov functional is related with impulse time sequence, which makes full use of the information on dynamical characteristic of synchronization error dynamics. Finally, a numerical example of typical chua’s system is given to illustrate the effectiveness and correctness of the theoretical results.

Impulsive Synchronization of Stochastic Neural Networks via Controlling Partial States

In the paper, synchronization problem for stochastic neural networks are studied by impulsively controlling partial states. At each impulsive instant, only part of the states are controlled to realize the synchronization of impulsively coupled stochastic neural networks. By using the method of average impulsive interval, less conservative synchronization criteria are derived. The derived sufficient conditions are closely related to the parameters of system dynamics, impulsive gain, impulsive interval and the proportion of the controlled components. Finally, numerical example is given to illustrate the effectiveness of our theoretical results.

Synchronization of chaotic Lur’e systems using sampled-data PD control

This paper investigates the problem of sampled-data PD control for master–slave synchronization of chaotic Lur’e systems with time delays and external disturbance. For delayed chaotic Lur’e systems, some new synchronization criteria are derived by constructing a new Lyapunov function based on the sampled-data PD control. Furthermore, some less conservative synchronization criteria for chaotic Lur’e systems are obtained by employing a tighter bound technique to estimate the derivative of the Lyapunov function. The proposed sampled-data controller is designed by linear matrix inequality approach. Finally, a numerical example is presented to demonstrate the effectiveness of the proposed method.

Synchronization criteria of chaotic Lur׳e systems with delayed feedback PD control

This paper is concerned with the problem of global asymptotical synchronization of chaotic Lur׳e systems by using a delayed feedback proportional-derivative (PD) control scheme. Based on Lyapunov functional approach, a stabilization condition for the synchronization error systems with delayed PD control is derived. The designed delayed PD feedback controller can ensure that the master and slave systems are asymptotically synchronous. The advantage of the constructed Lyapunov functional lies in the fact that it makes full use of the additional derivative state term. Furthermore, a less conservative synchronization criterion is proposed for the considered system only used proportional control. Compared with the existing ones, the merit of the proposed results in this paper lies in their reduced conservatism and application of the derivative control. The conditions represented in terms of linear matrix inequalities (LMIs) can be solved by the application of convex optimization algorithms. Finally, numerical examples are given to show the effectiveness of the proposed method and the improvement over some existing results.

Synchronization for distributed parameter NNs with mixed delays via sampled-data control

A sampled-data synchronization scheme is developed for a class of distributed parameter neural networks with mixed time delays. The design approach of the desired sampled data controller is also presented. We propose a sampled-data controller design, in which the sampled-data (in time) measurements of the state are taken in a finite number of fixed sampling points in the spatial domain. It is supposed that the sampling intervals in time and in space are bounded. Based on the extended Wirtinger’s inequality, an appropriate Lyapunov–Krasovskii functional and some free-weighting matrices are used to establish simple and less conservative synchronization criteria, which can ensure that the master systems synchronize with the slave systems via direct Lyapunov approach in terms of linear matrix inequalities. Finally, numerical simulations are carried out to demonstrate the effectiveness of the proposed synchronization method.

Semi-periodically intermittent control for synchronization of switched complex networks: a mode-dependent average dwell time approach

In this paper, we study the synchronization problem for switched complex networks with delayed coupling via semi-periodically intermittent control technique and a mode-dependent average dwell time method. The mathematical model of switched complex networks is established, and the networks switch among a finite number of subnetworks in accordance with a switching rule. By applying multiple Lyapunov function method and the mode-dependent average dwell time (MDADT) approach, less conservative synchronization criteria are derived based on a sequence of solvable linear matrix inequalities. Particularly, the conventional synchronization conditions are improved by using semi-periodically intermittent control and MDADT approach. Moreover, delayed coupling may affect the stability of the switched complex networks. In this paper, novel synchronization criteria are derived to deal with the relations between time delay and other parameters appropriately. Finally, a numerical example is provided to demonstrate the effectiveness of the derived theoretical results.

Novel integral inequality approach on master–slave synchronization of chaotic delayed Lur’e systems with sampled-data feedback control

This paper proposes a novel approach to study the problem of master–slave synchronization for chaotic delayed Lur’e systems with sampled-data feedback control. Specifically, first, it is assumed that the sampling intervals are randomly variable but bounded. By getting the utmost out of the usable information on the actual sampling pattern and the nonlinear part condition, a newly augmented Lyapunov–Krasovskii functional is constructed via a more general delay-partition approach. Second, in order to obtain less conservative synchronization criteria, a novel integral inequality is developed by the mean of the new adjustable parameters. Third, a longer sampling period is achieved by using a double integral form of Wirtinger-based integral inequality. Finally, three numerical examples with simulations of Chua’s circuit are given to demonstrate the effectiveness and merits of the proposed methods.

Outer synchronization of partially coupled dynamical networks via pinning impulsive controllers

This paper presents an analytical study of outer synchronization of partially coupled dynamical networks via pinning impulsive controller. At first, more realistic drive-response partially coupled networks are established. Then, based on the regrouping method, some efficient and less conservative synchronization criteria are derived and developed in terms of average impulsive interval. Our results show that, by impulsively controlling a crucial fraction of nodes in the response network, the outer synchronization can be achieved. Finally, illustrated examples are given to verify the effectiveness of the proposed strategy.

Synchronization of chaotic systems using fuzzy impulsive control

This paper investigates the problem of fuzzy impulsive control to synchronize two chaotic systems using a novel time-dependent Lyapunov function approach. Compared with the existing time-independent Lyapunov methods, the proposed method enables us to exploit more information on the impulsive intervals. Initially, using the Lyapunov technique and two parameterized linear matrix inequality (LMI) techniques, some less conservative synchronization criteria via a fuzzy impulsive controller using the states of both drive and response chaotic systems are derived. Subsequently, an LMI approach to designing such a fuzzy impulsive controller is developed to realize the synchronization. Finally, the proposed method is applied to the chaotic Lorenz system and Rosler system to illustrate its effectiveness.

Synchronization of Randomly Coupled Neural Networks With Markovian Jumping and Time-Delay

This paper studies synchronization in an array of coupled neural networks with Markovian jumping and random coupling strength. The array of neural networks are coupled in a random fashion which is governed by Bernoulli random variable and each node has an interval time-varying delay. By designing a novel Lyapunov functional, using some inequalities and the properties of random variables, several delay-dependent synchronization criteria are derived for the coupled networks of continuous-time version. Discrete-time analogues of the continuous-time networks are also formulated and studied. Some new lemmas are developed to obtain less conservative synchronization criteria of both continuous-time model and its discrete-time analogues. Numerical examples of both continuous-time system and its discrete-time analogues are finally given to demonstrate the effectiveness of the theoretical results.

Discontinuous Lyapunov functional approach to synchronization of time-delay neural networks using sampled-data

This paper investigates the synchronization problem of neural networks with time-varying delay under sampled-data control in the presence of a constant input delay. Based on the extended Wirtinger inequality, a discontinuous Lyapunov functional is introduced, which makes full use of the sawtooth structure characteristic of sampling input delay. A simple and less conservative synchronization criterion is given to ensure the master systems synchronize with the slave systems by using the linear matrix inequality (LMI) approach. The design method of the desired sampled-data controller is also proposed. Finally, two numerical examples are given to illustrate the effectiveness of the proposed methods.

Stochastic Synchronization of Complex Networks With Nonidentical Nodes Via Hybrid Adaptive and Impulsive Control

In this paper, the global exponential synchronization of delayed complex dynamical networks with nonidentical nodes and stochastic perturbations is studied. By combining adaptive control and impulsive control schemes, the considered network can be synchronized onto any given goal dynamics. The adaptive control is discontinuous and can overcome the unknown difference between dynamical nodes and goal system. As for the impulsive control, the concept named “average impulsive interval” with “elasticity number” of impulsive sequence is utilized to get less conservative synchronization criterion. Numerical simulations are given to show the effectiveness and less conservativeness of the theoretical results.

Synchronization of delayed complex dynamical networks with impulsive and stochastic effects

In this paper, the globally exponential synchronization of delayed complex dynamical networks with impulsive and stochastic perturbations is studied. The concept named “average impulsive interval” with “elasticity number” of impulsive sequence is introduced to get a less conservative synchronization criterion. By comparing with existing results, in which maximum or minimum of impulsive intervals are used to derive the synchronization criterion, the proposed synchronization criterion increases (or decreases) the impulse distances, which leads to the reduction of the control cost (or enhance the robustness of anti-interference) as the most important characteristic of impulsive synchronization techniques. It is discovered in our criterion that “elasticity number” has influence on synchronization of delayed complex dynamical networks but has no influence on that of non-delayed complex dynamical networks. Numerical simulations including a small-world network coupled with delayed Chua’s circuit are given to show the effectiveness and less conservativeness of the theoretical results.

Synchronization and exponential estimates of complex networks with mixed time-varying coupling delays

Exponential estimates and sufficient conditions for the exponential synchronization of complex dynamical networks with bounded time-varying delays are given in terms of linear matrix inequalities (LMIs). A generalized complex networks model involving both neutral delays and retarded ones is presented. The exponential synchronization problem of the complex networks is converted equivalently into the exponential stability problem of a group of uncorrelated delay functional differential equations with mixed time-varying delays. By utilizing the free weighting matrix technique, a less conservative delay-dependent synchronization criterion is derived. An illustrative example is provided to demonstrate the effectiveness of the proposed method.

A revisit to synchronization of Lurie systems with time-delay feedback control

This paper revisits the problem of synchronization for general Lurie systems with time-delay feedback control. Differently from most of existing results, the more restrictively slope restrictions on the nonlinearities of Lurie systems are considered in view of the fact that the slope restrictions may improve synchronization conditions compared with the sector ones. The Kalman–Yakubovich–Popov (KYP) lemma and the Schur complement formula are applied to get novel and less conservative synchronization criteria, which have the forms of linear matrix inequalities (LMIs). Numerical examples are presented to illustrate the efficiency of the proposed results.