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In this paper, we are concerned with the finite-time synchronization of a class of inertial neural networks with time delays. Without applying some finite-time stability theorems, which are widely applied to studying the finite-time synchronization for neural networks, by constructing two Lyapunov functions and using integral inequality method, two sufficient conditions on the finite-time synchronization for a class of inertial neural networks with time delays are derived. Considering that the method and research results of the finite-time synchronization are different from some existing works, this paper extends the works on the finite-time synchronization of neural networks. [ABSTRACT FROM AUTHOR]

This paper investigates the H\infty state estimation problem for a class of discrete-time nonlinear systems of the neural network type with random time-varying delays and multiple missing measurements. These nonlinear systems include recurrent neural networks, complex network systems, Lur’e systems, and so on which can be described by a unified model consisting of a linear dynamic system and a static nonlinear operator. The missing phenomenon commonly existing in measurements is assumed to occur randomly by introducing mutually individual random variables satisfying certain kind of probability distribution. Throughout this paper, first a Luenberger-like estimator based on the imperfect output data is constructed to obtain the immeasurable system states. Then, by virtue of Lyapunov stability theory and stochastic method, the H\infty performance of the estimation error dynamical system (augmented system) is analyzed. Based on the analysis, the H\infty estimator gains are deduced such that the augmented system is globally mean square stable. In this paper, both the variation range and distribution probability of the time delay are incorporated into the control laws, which allows us to not only have more accurate models of the real physical systems, but also obtain less conservative results. Finally, three illustrative examples are provided to validate the proposed control laws. [ABSTRACT FROM PUBLISHER]

This paper is concerned about the finite-time stabilizability and instabilizability for a class of delayed memristive neural networks (DMNNs). Through the design of a new nonlinear controller, algebraic criteria based on $M$ -matrix are established for the finite-time stabilizability of DMNNs, and the upper bound of the settling time for stabilization is estimated. In addition, finite-time instabilizability algebraic criteria are also established by choosing different parameters of the same nonlinear controller. The effectiveness and the superiority of the obtained results are supported by numerical simulations. [ABSTRACT FROM PUBLISHER]

Finite-time stability problem has been a hot topic in control and system engineering. This paper deals with the finite-time stabilization issue of memristor-based delayed neural networks (MDNNs) via two control approaches. First, in order to realize the stabilization of MDNNs in finite time, a delayed state feedback controller is proposed. Then, a novel adaptive strategy is applied to the delayed controller, and finite-time stabilization of MDNNs can also be achieved by using the adaptive control law. Some easily verified algebraic criteria are derived to ensure the stabilization of MDNNs in finite time, and the estimation of the settling time functional is given. Moreover, several finite-time stability results as our special cases for both memristor-based neural networks (MNNs) without delays and neural networks are given. Finally, three examples are provided for the illustration of the theoretical results. [ABSTRACT FROM PUBLISHER]

This paper considers the global exponential synchronization of drive-response memristive neural networks (MNNs) with heterogeneous time-varying delays. Because the parameters of MNNs are state-dependent, the MNNs may exhibit unexpected parameter mismatch when different initial conditions are chosen. Therefore, traditional robust control scheme cannot guarantee the synchronization of MNNs. Under the framework of Filippov solution, the drive and response MNNs are first transformed into systems with interval parameters. Then suitable controllers are designed to overcome the problem of mismatched parameters and synchronize the coupled MNNs. Based on some novel Lyapunov functionals and interval matrix inequalities, several sufficient conditions are derived to guarantee the exponential synchronization. Moreover, adaptive control is also investigated for the exponential synchronization. Numerical simulations are provided to illustrate the effectiveness of the theoretical analysis. [ABSTRACT FROM AUTHOR]

In this paper, the dissipative synchronization control problem for Markovian jump memristive neural networks (MNNs) is addressed with fully considering the time-varying delays and the fragility problem in the process of implementing the gain-scheduled controller. A Markov jump model is introduced to describe the stochastic changing among the connection of MNNs and it makes the networks under consideration suitable for some actual circumstances. By utilizing some improved integral inequalities and constructing a proper Lyapunov–Krasovskii functional, several delay-dependent synchronization criteria with less conservatism are established to ensure the dynamic error system is strictly stochastically dissipative. Based on these criteria, the procedure of designing the desired nonfragile gain-scheduled controller is established, which can well handle the fragility problem in the process of implementing the controller. Finally, an illustrated example is employed to explain that the developed method is efficient and available. [ABSTRACT FROM AUTHOR]

In this paper, multiple $\psi $ -type stability of Cohen–Grossberg neural networks (CGNNs) with both time-varying discrete delays and distributed delays is investigated. By utilizing $\psi $ -type functions combined with a new $\psi $ -type integral inequality for treating distributed delay terms, some sufficient conditions are obtained to ensure that multiple equilibrium points are $\psi $ -type stable for CGNNs with discrete and distributed delays, where the distributed delays include bounded and unbounded delays. These conditions of CGNNs with different output functions are less restrictive. More specifically, the algebraic criteria of the generalized model are applicable to several well-known neural network models by taking special parameters, and multiple different output functions are introduced to replace some of the same output functions, which improves the diversity of output results for the design of neural networks. In addition, the estimation of relative convergence rate of $\psi $ -type stability is determined by the parameters of CGNNs and the selection of $\psi $ -type functions. As a result, the existing results on multistability and monostability can be improved and extended. Finally, some numerical simulations are presented to illustrate the effectiveness of the obtained results. [ABSTRACT FROM AUTHOR]

This paper is concerned with global asymptotic stability of a neural network with a time-varying delay, where the delay function is differentiable uniformly bounded with delay-derivative bounded from above. First, a general reciprocally convex inequality is presented by introducing some slack vectors with flexible dimensions. This inequality provides a tighter bound in the form of a convex combination than some existing ones. Second, by constructing proper Lyapunov–Krasovskii functional, global asymptotic stability of the neural network is analyzed for two types of the time-varying delays depending on whether or not the lower bound of the delay derivative is known. Third, noticing that sufficient conditions on stability from estimation on the derivative of some Lyapunov–Krasovskii functional are affine both on the delay function and its derivative, allowable delay sets can be refined to produce less conservative stability criteria for the neural network under study. Finally, two numerical examples are given to substantiate the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

This paper investigates the estimator design for the neural networks, where distributed delays and imperfect measurements are included. A randomly occurred neuron-dependent nonlinearity is used to describe the uncertain measurements disturbed by neurons. The measurements are transmitted over multiple transmission channels, and Markov chains are introduced to model packet dropouts of these channels. A one-to-one map is constructed to transform $m$ independent Markov chains to an augmented one to facilitate system analysis. A new variable called channel state is defined based on the cases of packet dropouts, and the channel-state-dependent estimator is designed to trade off between the number and the performance of the estimator. Sufficient conditions are established to guarantee that the augmented system is stochastically stable and satisfies the strict $(Q, S, R)-\gamma -$ dissipativity. The estimator gains are derived using linear matrix methods. Finally, an example is applied to illustrate the effectiveness of the developed methods. [ABSTRACT FROM AUTHOR]

This paper investigates exponential stabilization of continuous-time dynamic systems (CDSs) via event-based impulsive control (EIC) approaches, where the impulsive instants are determined by certain state-dependent triggering condition. The global exponential stability criteria via EIC are derived for nonlinear and linear CDSs, respectively. It is also shown that there is no Zeno-behavior for the concerned closed loop control system. In addition, the developed event-based impulsive scheme is applied to the synchronization problem of master and slave memristive neural networks. Furthermore, a self-triggered impulsive control scheme is developed to avoid continuous communication between the master system and slave system. Finally, two numerical simulation examples are presented to illustrate the effectiveness of the proposed event-based impulsive controllers. [ABSTRACT FROM AUTHOR]

This paper addresses the problem of exponential synchronization of neural networks with time-varying delays. A sampled-data controller with stochastically varying sampling intervals is considered. The novelty of this paper lies in the fact that the control packet loss from the controller to the actuator is considered, which may occur in many real-world situations. Sufficient conditions for the exponential synchronization in the mean square sense are derived in terms of linear matrix inequalities (LMIs) by constructing a proper Lyapunov–Krasovskii functional that involves more information about the delay bounds and by employing some inequality techniques. Moreover, the obtained LMIs can be easily checked for their feasibility through any of the available MATLAB tool boxes. Numerical examples are provided to validate the theoretical results. [ABSTRACT FROM PUBLISHER]

This paper is concerned with the exponential synchronization for master–slave chaotic delayed neural network with event trigger control scheme. The model is established on a network control framework, where both external disturbance and network-induced delay are taken into consideration. The desired aim is to synchronize the master and slave systems with limited communication capacity and network bandwidth. In order to save the network resource, we adopt a hybrid event trigger approach, which not only reduces the data package sending out, but also gets rid of the Zeno phenomenon. By using an appropriate Lyapunov functional, a sufficient criterion for the stability is proposed for the error system with extended ( \mathcal X , \mathcal Y , \mathcal Z )-dissipativity performance index. Moreover, hybrid event trigger scheme and controller are codesigned for network-based delayed neural network to guarantee the exponential synchronization between the master and slave systems. The effectiveness and potential of the proposed results are demonstrated through a numerical example. [ABSTRACT FROM AUTHOR]

This paper studies the issue of robust state estimation for coupled neural networks with parameter uncertainty and randomly occurring distributed delays, where the polytopic model is employed to describe the parameter uncertainty. A set of Bernoulli processes with different stochastic properties are introduced to model the randomly occurrences of the distributed delays. Novel state estimators based on the local coupling structure are proposed to make full use of the coupling information. The augmented estimation error system is obtained based on the Kronecker product. A new Lyapunov function, which depends both on the polytopic uncertainty and the coupling information, is introduced to reduce the conservatism. Sufficient conditions, which guarantee the stochastic stability and the l2-l_\infty performance of the augmented estimation error system, are established. Then, the estimator gains are further obtained on the basis of these conditions. Finally, a numerical example is used to prove the effectiveness of the results. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the dissipativity and passivity of Markovian jump stochastic neural networks involving two additive time-varying delays. Using a Lyapunov–Krasovskii functional with triple and quadruple integral terms, we obtain delay-dependent passivity and dissipativity criteria for the system. Using a generalized Finsler lemma (GFL), a set of slack variables with special structure are introduced to reduce design conservatism. The dissipativity and passivity criteria depend on the upper bounds of the discrete time-varying delay and its derivative are given in terms of linear matrix inequalities, which can be efficiently solved through the standard numerical software. Finally, our illustrative examples show that the proposed method performs well and is successful in problems where existing methods fail. [ABSTRACT FROM PUBLISHER]

This paper investigates sampled-data synchronization problem of Markovian coupled neural networks with mode-dependent interval time-varying delays and aperiodic sampling intervals based on an enhanced input delay approach. A mode-dependent augmented Lyapunov–Krasovskii functional (LKF) is utilized, which makes the LKF matrices mode-dependent as much as possible. By applying an extended Jensen’s integral inequality and Wirtinger’s inequality, new delay-dependent synchronization criteria are obtained, which fully utilizes the upper bound on variable sampling interval and the sawtooth structure information of varying input delay. In addition, the desired stochastic sampled-data controllers can be obtained by solving a set of linear matrix inequalities. Finally, two examples are provided to demonstrate the feasibility of the proposed method. [ABSTRACT FROM PUBLISHER]

In this paper, the event-triggered state estimation problem is investigated for a class of discrete-time multidelayed neural networks with stochastic parameters and incomplete measurements. In order to cater for more realistic transmission process of the neural signals, we make the first attempt to introduce a set of stochastic variables to characterize the random fluctuations of system parameters. In the addressed neural network model, the delays among the interconnections are allowed to be different, which are more general than those in the existing literature. The incomplete information under consideration includes randomly occurring sensor saturations and quantizations. For the purpose of energy saving, an event-triggered state estimator is constructed and a sufficient condition is given under which the estimation error dynamics is exponentially ultimately bounded in the mean square. It is worth noting that the ultimate boundedness of the error dynamics is explicitly estimated. The characterization of the desired estimator gain is designed in terms of the solution to a certain matrix inequality. Finally, a numerical simulation example is presented to illustrate the effectiveness of the proposed event-triggered state estimation scheme. [ABSTRACT FROM AUTHOR]

This paper presents a new impulsive synchronization criterion of two identical reaction–diffusion neural networks with discrete and unbounded distributed delays. The new criterion is established by applying an impulse-time-dependent Lyapunov functional combined with the use of a new type of integral inequality for treating the reaction–diffusion terms. The impulse-time-dependent feature of the proposed Lyapunov functional can capture more hybrid dynamical behaviors of the impulsive reaction–diffusion neural networks than the conventional impulse-time-independent Lyapunov functions/functionals, while the new integral inequality, which is derived from Wirtinger’s inequality, overcomes the conservatism introduced by the integral inequality used in the previous results. Numerical examples demonstrate the effectiveness of the proposed method. Later, the developed impulsive synchronization method is applied to build a spatiotemporal chaotic cryptosystem that can transmit an encrypted image. The experimental results verify that the proposed image-encrypting cryptosystem has the advantages of large key space and high security against some traditional attacks. [ABSTRACT FROM PUBLISHER]

This paper deals with the lag synchronization problem of memristor-based coupled neural networks with or without parameter mismatch using two different algorithms. Firstly, we consider the memristor-based neural networks with parameter mismatch, lag complete synchronization cannot be achieved due to parameter mismatch, the concept of lag quasi-synchronization is introduced. Based on the $\omega $ -measure method and generalized Halanay inequality, the error level is estimated, a new lag quasi-synchronization scheme is proposed to ensure that coupled memristor-based neural networks are in a state of lag synchronization with an error level. Secondly, by constructing Lyapunov functional and applying common Halanary inequality, several lag complete synchronization criteria for the memristor-based neural networks with parameter match are given, which are easy to verify. Finally, two examples are given to illustrate the effectiveness of the proposed lag quasi-synchronization or lag complete synchronization criteria, which well support theoretical results. [ABSTRACT FROM PUBLISHER]

This paper investigates the problem of sampled-data stabilization for neural-network-based control systems with an optimal guaranteed cost. Using time-dependent Lyapunov functional approach, some novel conditions are proposed to guarantee the closed-loop systems exponentially stable, which fully use the available information about the actual sampling pattern. Based on the derived conditions, the design methods of the desired sampled-data three-layer fully connected feedforward neural-network-based controller are established to obtain the largest sampling interval and the smallest upper bound of the cost function. A practical example is provided to demonstrate the effectiveness and feasibility of the proposed techniques. [ABSTRACT FROM AUTHOR]

This paper is concerned with the problems of exponential stability analysis and synchronization of discrete-time switched delayed neural networks. Using the average dwell time approach together with the piecewise Lyapunov function technique, sufficient conditions are proposed to guarantee the exponential stability for the switched neural networks with time-delays. Benefitting from the delay partitioning method and the free-weighting matrix technique, the conservatism of the obtained results is reduced. In addition, the decay estimates are explicitly given and the synchronization problem is solved. The results reported in this paper not only depend upon the delay, but also depend upon the partitioning, which aims at reducing the conservatism. Numerical examples are presented to demonstrate the usefulness of the derived theoretical results. [ABSTRACT FROM PUBLISHER]

In this paper, a dynamic delay interval (DDI) method is proposed to deal with the stability problem of neural networks with two delay components. This method extends the fixed interval of a time-varying delay to a dynamic one, which relaxes the restriction on upper and lower bounds of the delay intervals. Combining the reciprocally convex combination technique and Wirtinger integral inequality, the DDI method leads to some much less conservative delay-dependent stability criteria based on a linear matrix inequality for neural networks with two delay components. Furthermore, the criteria for the system with a single time-varying delay are provided. Some examples are given to illustrate the effectiveness of the obtained results. [ABSTRACT FROM AUTHOR]

This paper revisits the problem of asymptotic stability analysis for neural networks with distributed delays. The distributed delays are assumed to be constant and prescribed. Since a positive-definite quadratic functional does not necessarily require all the involved symmetric matrices to be positive definite, it is important for constructing relaxed Lyapunov–Krasovskii functionals, which generally lead to less conservative stability criteria. Based on this fact and using two kinds of integral inequalities, a new delay-dependent condition is obtained, which ensures that the distributed delay neural network under consideration is globally asymptotically stable. This stability criterion is then improved by applying the delay partitioning technique. Two numerical examples are provided to demonstrate the advantage of the presented stability criteria. [ABSTRACT FROM PUBLISHER]

In this article, the finite-time synchronization (FTSYN) of a class of quaternion-valued neural networks (QVNNs) with discrete and distributed time delays is studied. Furthermore, the FTSYN and fixed-time synchronization (FIXSYN) of the QVNNs without time delay are investigated. Different from the existing results, which used decomposition techniques, by introducing an improved one-norm, we use a direct analytical method to study the synchronization problems. Incidentally, several properties of one-norm of the quaternion are analyzed, and then, three effective controllers are proposed to synchronize the drive and response QVNNs within a finite time or fixed time. Moreover, efficient criteria are proposed to guarantee that the synchronization of QVNNs with or without mixed time delays can be realized within a finite and fixed time interval, respectively. In addition, the settling times are reckoned. Compared with the existing work, our advantages are mainly reflected in the simpler Lyapunov analytical process and more general activation function. Finally, the validity and practicability of the conclusions are illustrated via four numerical examples. [ABSTRACT FROM AUTHOR]

A correction to the article "LMI Approach for Global Periodicity of Neural Networks With Time-Varying Delays," published in a previous issue is presented.

In this brief, the problem of delay-dependent stability of recurrent neural networks with time-varying delays is studied. A newly augmented Lyapunov–Krasovskii functional (LKF) that considers the information of the nonzero lower bound of time-varying delays is developed. Moreover, the information of the delayed state terms is not considered as elements of augmented vectors when constructing the LKF. An improved stability criterion with the framework of linear matrix inequalities is derived by employing the integral inequality and reciprocally convex combination. With the comparison to the existing ones, the developed stability criterion for neural networks has less conservatism and complexity. Finally, two widely used numerical examples are given to show the effectiveness and superiority of the obtained stability criterion. [ABSTRACT FROM AUTHOR]

This brief is concerned with global asymptotic stability of a neural network with a time-varying delay. First, by introducing an auxiliary vector with some nonorthogonal polynomials, a slack-matrix-based integral inequality is established, which includes some existing one as its special case. Second, a novel Lyapunov–Krasovskii functional is constructed to suit for the use of the obtained integral inequality. As a result, a less conservative stability criterion is derived, whose effectiveness is finally demonstrated through two well-used numerical examples. [ABSTRACT FROM AUTHOR]

This brief addresses the problem of global dissipativity analysis of nonautonomous neural networks with multiple proportional delays. By using a novel constructive approach based on some comparison techniques for differential inequalities, new explicit delay-independent conditions are derived using M-matrix theory to ensure the existence of generalized exponential attracting sets and the global dissipativity of the system. The method presented in this brief is also utilized to derive a generalized exponential estimate for a class of Halanay-type inequalities with proportional delays. Finally, three numerical examples are given to illustrate the effectiveness and improvement of the obtained results. [ABSTRACT FROM AUTHOR]