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Synchronization is a key topic of research in neuroscience, medicine, and artificial neural networks; however, understanding its principle is difficult, both scientifically and mathematically. Specifically, the synchronization of the FitzHugh-Nagumo network with a hierarchical architecture has previously been studied; however, a mathematical analysis has not been conducted, owing to the network complexity. Therefore, in this paper, we saught to understand synchronization through mathematical analyses. In particular, we consider the most common types of hierarchical architecture and present a condition of the hierarchical architecture to induce synchronization. First, we provide mathematical analyses of a Lyapunov function for each layer, from which we obtain sufficient conditions guaranteeing synchronization and show that the Lyapunov function decreases exponentially. Moreover, we show that the internal connectivity critically affects synchronization in the first layer; however, in the second and subsequent layers, the internal connectivity is not important for synchronization, and the connectivity up to the first layer critically affects synchronization. We expect that the results and mathematical methodology can be applied to study other similar neural models with hierarchical architectures. [ABSTRACT FROM AUTHOR]

This paper deals with a class of fractional-order octonion-valued neural networks (FOOVNNs) with impulsive effects. Firstly, although the multiplication of octonion numbers does not satisfy the commutativity and associativity, we don't need to separate an octonion-valued system into eight real-valued systems. Secondly, by applying the appropriate Lyapunov function, and inequality techniques, we obtain the global asymptotical synchronization of FOOVNNs. Finally, we give two illustrative examples to illustrate the feasibility of the proposed method. [ABSTRACT FROM AUTHOR]

In this paper, we present adaptive neural network tracking control of a robotic manipulator with input deadzone and output constraint. A barrier Lyapunov function is employed to deal with the output constraints. Adaptive neural networks are used to approximate the deadzone function and the unknown model of the robotic manipulator. Both full state feedback control and output feedback control are considered in this paper. For the output feedback control, the high gain observer is used to estimate unmeasurable states. With the proposed control, the output constraints are not violated, and all the signals of the closed loop system are semi-globally uniformly bounded. The performance of the proposed control is illustrated through simulations. [ABSTRACT FROM PUBLISHER]

This paper investigates the problem of the dynamical behaviours of a class of complex-valued neural networks with mixed time delays and impulsive effect. By separating the complex-valued neural networks into the real and the imaginary parts, the corresponding equivalent real-valued systems are obtained. Some sufficient conditions are derived for assuring the exponential stability of the equilibrium point of the system based on the vector Lyapunov function method and mathematical induction method. The obtained results generalise the existing ones. Finally, two numerical examples with simulations are given to demonstrate the feasibility of the proposed results. [ABSTRACT FROM PUBLISHER]

This paper investigates the global attractive set of neural networks with neutral item. To better deal with the neutral terms, different types of activation functions are considered. Based on matrix measures, inequality techniques, and Lyapunov theory, three new types of Lyapunov functions are designed to find the global attractive set of the system. We give out a simulation example to verify the validity of theory results. The result is very inclusive, whether the system has equilibrium or not. As long as the system is stable, we can find its global attractive set. [ABSTRACT FROM AUTHOR]

This paper mainly studies the globally fixed-time synchronization of a class of coupled neutral-type neural networks with mixed time-varying delays via discontinuous feedback controllers. Compared with the traditional neutral-type neural network model, the model in this paper is more general. A class of general discontinuous feedback controllers are designed. With the help of the definition of fixed-time synchronization, the upper right-hand derivative and a defined simple Lyapunov function, some easily verifiable and extensible synchronization criteria are derived to guarantee the fixed-time synchronization between the drive and response systems. Finally, two numerical simulations are given to verify the correctness of the results. [ABSTRACT FROM AUTHOR]

In this paper, a novel fuzzy neural network structure for uncertain nonlinear systems is proposed. This network is called wavelet Takagi–Sugeno–Kang (TSK) fuzzy cerebellar model neural network, which includes the framework of a cerebellar model neural network (CMNN) and the wavelet-function-based TSK fuzzy inference model. In order to effectively solve the uncertainty problem of nonlinear systems, a new structure is proposed where the wavelet function is used in the consequent parts of TSK-type fuzzy CMNN instead of the linear combination of the input variables in the traditional TSK fuzzy systems. This structure combines the advantages of the wavelet function, the CMNN and the TSK fuzzy inference system; thus, it is a more effective model for the uncertain nonlinear systems. In order to provide fast training, parameter update laws of the proposed model are derived based on the gradient descent method in which the learning-rates are online adapted. Furthermore the Lyapunov function is used to analyze the convergence of the considered systems. Finally, four different types of applications are applied to demonstrate the effectiveness of the proposed model. The simulation comparisons with other neural network models have verified the effectiveness of the new model. [ABSTRACT FROM AUTHOR]

This paper concentrates on the problem of global exponential periodicity and stability of memristive neural networks with variable delays. By constructing the appropriate Lyapunov functionals and utilizing some inequality techniques, new algebraic criteria are proposed to guarantee the existence and global exponential stability of periodic solution of the considered system. In addition, the proposed theoretical results not only expand and complement the earlier publications, but also are easy to be checked with the parameters of system itself. A numerical example is given to demonstrate the effectiveness of our results. [ABSTRACT FROM AUTHOR]

In this paper, several simple and new conditions are presented to ensure existence, uniqueness and global exponential robust stability of the equilibrium point of neural networks with delays by using contraction mapping principle, homeomorphism property and Lyapunov method. The conditions given in this paper are easy to verify and apply, and the obtained results improve and extend to those in the literature. In addition, two examples are given to show the effectiveness of the proposed results. [ABSTRACT FROM AUTHOR]

This paper presents an adaptive control strategy for a unified chaotic system with unknown functions and full state constraints. The unknown functions in the unified chaotic system are approximated by using the radial basis function neural networks. At present, a great many of the results for chaotic system neglect the situation of full state constraints. In the proposed scheme, we successfully utilize the barrier Lyapunov function approach to prevent the full state from violating constraint condition. In addition, when the full state constraints are considered, the computation online burden is very large in the previous works. In contrast with the existing results for unified chaotic system, the number of the adaptation laws has only two. The state feedback controllers and the adaptive laws for estimating the uncertainties were derived based on the Lyapunov stability theory. Finally, it is proved that all the signals in the unified chaotic system are bounded and the constraints are not violated. The performance of the proposed scheme was validated by using a simulation example. [ABSTRACT FROM AUTHOR]

In this paper, generalized lag synchronization (GLS) for a class of neural networks with discontinuous activation functions and bounded external disturbances is studied under the framework of Filippov solutions. The external disturbances to the driver and response neural networks are nonidentical. A simple discontinuous adaptive controller is designed to overcome the difficulty induced by the nonidentical perturbations and the uncertainties of the Filippov solutions. Based on the concept of Filippov solutions, differential inclusion, nonsmooth analysis, and Lyapunov function method, sufficient conditions are obtained to guarantee the GLS of the discontinuous neural networks. Some existing results on synchronization of neural networks with discontinuous activations are extended and improved. Results of this paper are also applicable to nonlinear continuous systems. Numerical simulations are given to show the effectiveness of the theoretical results. [ABSTRACT FROM AUTHOR]

In this paper, we have integrated the passivity of delayed neural networks with discontinuous activations which are unbounded. Based on differential inclusion theory and nonsmooth analysis, some sufficient conditions are presented by means of the generalized Lyapunov method. The results are established in form of linear matrix inequality. In addition, Some numerical examples are proposed to show the effectiveness of the developed results. [ABSTRACT FROM AUTHOR]

In this paper, a trajectory tracking control law is proposed for a class of marine surface vessels in the presence of full-state constraints and dynamics uncertainties. A barrier Lyapunov function (BLF) based control is employed to prevent states from violating the constraints. Neural networks are used to approximate the system uncertainties in the control design, and the control law is designed by using the Moore-Penrose inverse. The proposed control is able to compensate for the effects of full-state constraints. Meanwhile, the signals in the closed-loop system are guaranteed to be semiglobally uniformly bounded, with the asymptotic tracking being achieved. Finally, the performance of the proposed control has been tested and verified by simulation studies. [ABSTRACT FROM PUBLISHER]

In this paper, a novel decentralized adaptive neural control scheme is proposed for a class of interconnected large-scale uncertain nonlinear time-delay systems with input saturation. Radial basis function ( RBF) neural networks ( NNs) are used to tackle unknown nonlinear functions. Then, the decentralized adaptive NN tracking controller is constructed by combining Lyapunov- Krasovskii functions and the dynamic surface control ( DSC) technique, along with the minimal-learning-parameters ( MLP) algorithm. The stability analysis subject to the effect of input saturation constraints are conducted with the help of an auxiliary design system based on the Lyapunov- Krasovskii method. The proposed controller guarantees uniform ultimate boundedness ( UUB) of all of the signals in the closed-loop large-scale system, while the tracking errors converge to a small neighborhood around the origin. An advantage of the proposed control scheme lies in the number of adaptive parameters of the whole system being reduced to one and in the solution of the three problems of 'computational explosion,' 'dimension curse,' and 'controller singularity'. Finally, simulation results along with comparisons are presented to demonstrate the advantages, effectiveness, and performance of the proposed scheme. [ABSTRACT FROM AUTHOR]

This paper considers the asymptotic stability problem for a class of neural networks with discrete and distributed delays. Based on a new augmented Lyapunov functional and integral inequalities, the new asymptotic stability condition is established in terms of linear matrix inequality. Meanwhile, the importance of some augmented terms in the Lyapunov functional are discussed. Compared with previous methods to deal with the distributed delay, our method is less conservative due to the use of the new Lyapunov functional. Finally, numerical examples illustrate the relaxation of obtained results and our claims. [ABSTRACT FROM PUBLISHER]

In this paper, the problem of the global asymptotic stability (GAS) of a class of delayed neural network is investigated. Under the generalization of dropping the boundedness and differentiability hypotheses for activation functions, using some existing results for the existence and uniqueness of the equilibrium point, we obtain a couple of general results concerning GAS by means of Lyapunov functional method without the assumption of symmetry of interconnection matrix. Our results improve and extend some previous works of other researchers. Moreover, our conditions are presented in terms of system parameters, which have leading significance in designs and applications of GAS for Hopfield neural network (HNNs) and delayed cellular neural network (DCNNs). [ABSTRACT FROM AUTHOR]

In this paper, adaptive neural tracking control is proposed for a robotic manipulator with uncertainties in both manipulator dynamics and joint actuator dynamics. The manipulator joints are subject to inequality constraints, i.e., the joint angles are required to remain in some compact sets. Integral barrier Lyapunov functionals (iBLFs) are employed to address the joint space constraints directly without performing an additional mapping to the error space. Neural networks (NNs) are utilised to compensate for the unknown robot dynamics and external force. Adapting parameters are developed to estimate the unknown bounds on NN approximations. By the Lyapunov synthesis, the proposed control can guarantee the semi-global uniform ultimate boundedness of the closed-loop system, and the practical tracking of joint reference trajectory is achieved without the violation of predefined joint space constraints. Simulation results are given to validate the effectiveness of the proposed control scheme. [ABSTRACT FROM AUTHOR]

Inductive power transfer (IPT) systems facilitate contactless power transfer between two sides and across an air-gap, through weak magnetic coupling. However, IPT systems constitute a high order resonant circuit and, as such, are difficult to design and control. Aiming at the control problems for bidirectional IPT system, a neural networks based proportional-integral-derivative (PID) control strategy is proposed in this paper. In the proposed neural PID method, the PID gains, $$K_{P}$$ , $$K_{I}$$ and $$K_{D}$$ are treated as Gaussian potential function networks (GPFN) weights and they are adjusted using online learning algorithm. In this manner, the neural PID controller has more flexibility and capability than conventional PID controller with fixed gains. The convergence of the GPFN weights learning is guaranteed using Lyapunov method. Simulations are used to test the effective performance of the proposed controller. [ABSTRACT FROM AUTHOR]

Summary: This paper introduces a multiple‐input–single‐output (MISO) neuro‐fractional‐order Hammerstein (NFH) model with a Lyapunov‐based identification method, which is robust in the presence of outliers. The proposed model is composed of a multiple‐input–multiple‐output radial basis function neural network in series with a MISO linear fractional‐order system. The state‐space matrices of the NFH are identified in the time domain via the Lyapunov stability theory using input‐output data acquired from the system. In this regard, the need for the system state variables is eliminated by introducing the auxiliary input‐output filtered signals into the identification laws. Moreover, since practical measurement data may contain outliers, which degrade performance of the identification methods (eg, least‐square–based methods), a Gaussian Lyapunov function is proposed, which is rather insensitive to outliers compared with commonly used quadratic Lyapunov function. In addition, stability and convergence analysis of the presented method is provided. Comparative example verifies superior performance of the proposed method as compared with the algorithm based on the quadratic Lyapunov function and a recently developed input‐output regression‐based robust identification algorithm. [ABSTRACT FROM AUTHOR]

Summary: This paper is concerned with the problem of state estimation for a class of neural networks with discrete and distributed interval time‐varying delays. We propose a new approach of nonlinear estimator design for the class of neutral‐type neural networks. By constructing a newly augmented Lyapunov‐Krasovskii functional, we establish sufficient conditions to guarantee the estimation error dynamics to be globally exponentially stable. The obtained results are formulated in terms of linear matrix inequalities (LMIs), which can be easily verified by the MATLAB LMI control toolbox. Then, the desired estimators gain matrix is characterized in terms of the solution to these LMIs. Three numerical examples are given to show the effectiveness of the proposed design method. [ABSTRACT FROM AUTHOR]

In this paper, we consider a class of delayed quaternion‐valued cellular neural networks (DQVCNNs) with impulsive effects. By using a novel continuation theorem of coincidence degree theory, the existence of anti‐periodic solutions for DQVCNNs is obtained with or without assuming that the activation functions are bounded. Furthermore, by constructing a suitable Lyapunov function, some sufficient conditions are derived to guarantee the global exponential stability of anti‐periodic solutions for DQVCNNs. Our results are new and complementary to the known results even when DQVCNNs degenerate into real‐valued or complex‐valued neural networks. Finally, an example is given to illustrate the effectiveness of the obtained results. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the passivity problem of delayed neural networks, where the activation functions are discontinuous. Based on differential inclusion theory, sufficient conditions for this problem are obtained by means of generalized Lyapunov approach. The theoretical results can be checked by solving some linear matrix inequalities. The results extend previous researches on the passivity of delayed neural networks. [ABSTRACT FROM AUTHOR]

This paper studies the problem of designing observer-based controllers for a class of delayed neural networks with nonlinear observation. The system under consideration is subject to nonlinear observation and an interval time-varying delay. The nonlinear observation output is any nonlinear Lipschitzian function and the time-varying delay is not required to be differentiable nor its lower bound be zero. By constructing a set of appropriate Lyapunov-Krasovskii functionals and utilizing the Newton-Leibniz formula, some delay-dependent stabilizability conditions which are expressed in terms of Linear Matrix Inequalities (LMIs) are derived. The derived conditions allow simultaneous computation of two bounds that characterize the exponential stability rate of the closed-loop system. The unknown observer gain and the state feedback observer-based controller are directly obtained upon the feasibility of the derived LMIs stabilizability conditions. A simulation example is presented to verify the effectiveness of the proposed result. [ABSTRACT FROM AUTHOR]

In the conventional adaptive neural network control of robotic manipulator, the desired position of robot end effector is specified as a point or trajectory. In addition, it is usually difficult to guarantee the transient performance of adaptive neural network control system due to the initialization error of the weight of neural network. In this paper, a new control formulation is proposed for the adaptive neural network control of robotic manipulator, which unifies existing neural network control tasks such as setpoint control, trajectory tracking control, and trajectory tracking control with prescribed performance bound. The proposed method also includes a new adaptive neural network control scheme where the objective for the robot end effector can be specified as a dynamic region, instead of the desired position or trajectory. The stability of the closed-loop system is analyzed using Lyapunov-like analysis. Experimental results are presented to illustrate the performance of the proposed approach and the energy-saving property of the proposed neural network controller with dynamic region. [ABSTRACT FROM AUTHOR]

In this paper, an adaptive reinforcement learning-based solution is developed for the infinite-horizon optimal control problem of constrained-input continuous-time nonlinear systems in the presence of nonlinearities with unknown structures. Two different types of neural networks (NNs) are employed to approximate the Hamilton–Jacobi–Bellman equation. That is, an recurrent NN is constructed to identify the unknown dynamical system, and two feedforward NNs are used as the actor and the critic to approximate the optimal control and the optimal cost, respectively. Based on this framework, the action NN and the critic NN are tuned simultaneously, without the requirement for the knowledge of system drift dynamics. Moreover, by using Lyapunov’s direct method, the weights of the action NN and the critic NN are guaranteed to be uniformly ultimately bounded, while keeping the closed-loop system stable. To demonstrate the effectiveness of the present approach, simulation results are illustrated. [ABSTRACT FROM PUBLISHER]

Abstract This paper carries out a theoretical investigation of the class of neutral-type delayed Cohen–Grossberg neural networks by using the Lyapunov stability theory. By employing a suitable Lyapunov functional candidate, we derive some new delay independent sufficient conditions for the global asymptotic stability of the equilibrium point for the neutral-type Cohen–Grossberg neural networks with time delays. The obtained stability conditions can be completely characterized by the networks parameters of the neutral systems under consideration. Therefore, it is easy to verify the applicability of our results by simply using some algebraic manipulations of the conditions. Some numerical examples are also given to show the effectiveness of the derived analytical results. A detailed comparison between our proposed results and recently reported corresponding stability results is also made, revealing that the conditions given in this paper establish a new set of stability criteria for Neutral-Type Cohen–Grossberg Neural Networks. [ABSTRACT FROM AUTHOR]

In this paper, the synchronization problem of fractional-order complex-valued neural networks with discrete and distributed delays is investigated. Based on the adaptive control and Lyapunov function theory, some sufficient conditions are derived to ensure the states of two fractional-order complex-valued neural networks with discrete and distributed delays achieve complete synchronization rapidly. Finally, numerical simulations are given to illustrate the effectiveness and feasibility of the theoretical results. [ABSTRACT FROM AUTHOR]

This paper deals with the H control problem of neural networks with time-varying delays. The system under consideration is subject to time-varying delays and various activation functions. Based on constructing some suitable Lyapunov-Krasovskii functionals, we establish new sufficient conditions for H control for two cases of time-varying delays: (1) the delays are differentiable and have an upper bound of the delay-derivatives and (2) the delays are bounded but not necessary to be differentiable. The derived conditions are formulated in terms of linear matrix inequalities, which allow simultaneous computation of two bounds that characterize the exponential stability rate of the solution. Numerical examples are given to illustrate the effectiveness of our results. [ABSTRACT FROM AUTHOR]

This paper deals with the robust stability problem of uncertain stochastic neural networks of neutral-type with interval time-varying delays. The uncertainties under consideration are norm-bounded, and the delay is assumed to be time-varying and belongs to a given interval. By using the Lyapunov-Krasovskill functional method and the linear matrix inequality (LMI) technique, the novel stability criteria are derived in terms of LMI. Finally, numerical examples are provided to demonstrate the effectiveness of the proposed criteria. [ABSTRACT FROM AUTHOR]

This paper is concerned with a delay-dependent state estimator for neutral-type neural networks with mixed time-varying delays and Markovian jumping parameters. The addressed neural networks have a finite number of modes, and the modes may jump from one to another according to a Markov process. By construction of a suitable Lyapunov- Krasovskii functional, a delay-dependent condition is developed to estimate the neuron states through available output measurements such that the estimation error system is globally asymptotically stable in a mean square. The criterion is formulated in terms of a set of linear matrix inequalities (LMIs), which can be checked efficiently by use of some standard numerical packages. [ABSTRACT FROM AUTHOR]

This paper is concerned with the passivity and stability problems of reaction-diffusion neural networks (RDNNs) in which the input and output variables are varied with the time and space variables. By utilizing the Lyapunov functional method combined with the inequality techniques, some sufficient conditions ensuring the passivity and global exponential stability are derived. Furthermore, when the parameter uncertainties appear in RDNNs, several criteria for robust passivity and robust global exponential stability are also presented. Finally, a numerical example is provided to illustrate the effectiveness of the proposed criteria. [ABSTRACT FROM PUBLISHER]

In this paper, passivity analysis is conducted for discrete-time stochastic neural networks with both Markovian jumping parameters and mixed time delays. The mixed time delays consist of both discrete and distributed delays. The Markov chain in the underlying neural networks is finite piecewise homogeneous. By introducing a Lyapunov functional that accounts for the mixed time delays, a delay-dependent passivity condition is derived in terms of the linear matrix inequality approach. The case of Markov chain with partially unknown transition probabilities is also considered. All the results presented depend upon not only discrete delay but also distributed delay. A numerical example is included to demonstrate the effectiveness of the proposed methods. [ABSTRACT FROM AUTHOR]

In this paper, we study the problem of global asymptotic stability of the equilibrium of a class of neural networks with supremum and fixed moments of impulsive effect. We establish stability criteria by employing Lyapunov functions and Razumikhin technique. [ABSTRACT FROM AUTHOR]

In this paper, the dynamic behaviors of a class of neural networks with time-varying delays are investigated. Some less weak sufficient conditions based on p-norm and ∞-norm are obtained to guarantee the existence, uniqueness of the equilibrium point for the addressed neural networks without impulsive control by applying homeomorphism theory. And then, by utilizing inequality technique, Lyapunov functional method and the analysis method, some new and useful criteria of the globally exponential stability with respect to the equilibrium point under impulsive control we assumed are derived based on p-norm and ∞-norm, respectively. Finally, an example with simulation is given to show the effectiveness of the obtained results. [ABSTRACT FROM AUTHOR]

The paper studies the design and analysis of a neural adaptive control strategy for a class of square nonlinear bioprocesses with incompletely known and time-varying dynamics. In fact, an adaptive controller based on a dynamical neural network used as a model of the unknown plant is developed. The neural controller design is achieved by using an input–output feedback linearization technique. The adaptation laws of neural network weights are derived from a Lyapunov stability property of the closed-loop system. The convergence of the system tracking error to zero is guaranteed without the need of network weights convergence. The resulted control method is applied in a depollution control problem in the case of a wastewater treatment bioprocess, belonging to the square nonlinear class, for which kinetic dynamics are strongly nonlinear, time varying and not exactly known. [ABSTRACT FROM AUTHOR]

In this paper, we consider the problem of exponential stability for recurrent neural networks with multiple time-varying delays and reaction-diffusion terms. The activation functions are supposed to be bounded and globally Lipschitz continuous. By means of Lyapunov functionals, sufficient conditions are derived, which guarantee global exponential stability of the delayed neural network. Finally, a numerical example is given to show the correctness of our analysis. [ABSTRACT FROM AUTHOR]

This correspondence paper focuses on the problem of exponential stability for neural networks with a time-varying delay. The relationship among the time-varying delay, its upper bound, and their difference is taken into account. As a result, an improved linear-matrix- inequality-based delay-dependent exponential stability criterion is obtained without ignoring any terms in the derivative of Lyapunov- Krasovskii functional. Two numerical examples are given to demonstrate its effectiveness. [ABSTRACT FROM AUTHOR]

In this paper we investigate the drive-response type synchronization of Hopfield-type neural networks with connection time delays for both discrete and distributed cases. By employing the Lyapunov functional method, we propose a sufficient condition to ensure the occurrence of synchronization with exponential rates. This criterion is independent of time delays as well as the types of delay. We prove that the exponential synchronization occurs provided a certain weighted sum of the connection and coupling strengths is negative enough, no matter that the connection time delay is of discrete or distributed case. Numerical examples are provided to illustrate the results. [ABSTRACT FROM AUTHOR]

In the present paper the question of global asymptotic stability of a class of impulsive delayed cellular neural networks with dynamical thresholds is considered. The main results are obtained by means of piecewise continuous Lyapunov functions. The Razumikhin technique is used. [ABSTRACT FROM AUTHOR]

This paper presents an artificial neural network to solve the quadratic zero-one programming problems under linear constraints. In this paper, by using the connection between integer and nonlinear programming, the quadratic zero-one programming problem is transformed into the quadratic programming problem with nonlinear constraints. Then, by using the nonlinear complementarity problem (NCP) function and penalty method this problem is transformed into an unconstrained optimization problem. It is shown that the Hessian matrix of the associated function in the unconstrained optimization problem is positive definite in the optimal point. To solve the unconstrained optimization problem an artificial neural network is used. The proposed neural network has a simple structure and a low complexity of implementation. It is shown here that the proposed artificial neural network is stable in the sense of Lyapunov. Finally, some numerical examples are given to show that the proposed model finds the optimal solution of this problem in the low convergence time. [ABSTRACT FROM AUTHOR]

In this paper, the exponential stability for a class of neural networks with time-varying delay is concerned. An improved integral inequality is derived which extends the auxiliary function-based integral inequality. A novel Lyapounov-Krasovskii functional (LKF) with some new integral terms is constructed. Based on the improved integral inequality and reciprocally convex combination approach, a less conservative exponential stability criterion for the neural networks with time-varying delay is obtained. The effectiveness of the proposed method in this paper is illustrated via numerical examples. [ABSTRACT FROM AUTHOR]

In this paper, the exponential stability of anti-periodic solutions for inertial neural networks with time delays is investigated. First, by properly chosen variable substitution the system is transformed to first order differential equation. Second, some sufficient conditions which can ensure the existence and exponential stability of anti-periodic solutions for the system are obtained by using Lyapunov method and uniformly converges. Finally, an example is given to illustrate the effectiveness of the results. [ABSTRACT FROM AUTHOR]