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This paper focuses on the problem of stability analysis for Memristor-based generalized neural networks (MGNNs) with time-varying delay. The conventional memristor-based neural networks (MNNs) can be regarded as a special case of MGNNs. The paper proposes an improved auxiliary function-based integral inequality to address the derivative of the triple integral within the Lyapunov-Krasovskii functional (LKF). This advanced inequality encompasses well-known integral inequalities as special cases and reduces conservatism by incorporating additional free matrices. Based on the improved integral inequality, the stability criteria with less conservatism for MGNNs are derived by making full use of the information of state and activation function. Finally, the feasibility and superiority of the proposed methods can be demonstrated with three numerical examples. [ABSTRACT FROM AUTHOR]

This article investigates the finite-time decentralized event-triggered feedback control problem for generalized neural networks (GNNs) with mixed interval time-varying delays and cyber-attacks. A decentralized event-triggered method reduces the network transmission load and decides whether sensor measurements should be sent out. The cyber-attacks that occur at random are described employing Bernoulli distributed variables. By the Lyapunov-Krasovskii stability theory, we apply an integral inequality with an exponential function to estimate the derivative of the Lyapunov-Krasovskii functionals (LKFs). We present new sufficient conditions in the form of linear matrix inequalities. The main objective of this research is to investigate the stochastic finite-time boundedness of GNNs with mixed interval time-varying delays and cyber-attacks by providing a decentralized event-triggered method and feedback controller. Finally, a numerical example is constructed to demonstrate the effectiveness and advantages of the provided control scheme.

This article investigates the finite-time decentralized event-triggered feedback control problem for generalized neural networks (GNNs) with mixed interval time-varying delays and cyberattacks. A decentralized event-triggered method reduces the network transmission load and decides whether sensor measurements should be sent out. The cyber-attacks that occur at random are described employing Bernoulli distributed variables. By the Lyapunov-Krasovskii stability theory, we apply an integral inequality with an exponential function to estimate the derivative of the Lyapunov-Krasovskii functionals (LKFs). We present new sufficient conditions in the form of linear matrix inequalities. The main objective of this research is to investigate the stochastic finite-time boundedness of GNNs with mixed interval time-varying delays and cyber-attacks by providing a decentralized event-triggered method and feedback controller. Finally, a numerical example is constructed to demonstrate the effectiveness and advantages of the provided control scheme. [ABSTRACT FROM AUTHOR]

Abstract This article investigates new delay-dependent finite-time boundedness for generalized neural networks (GNNs) with mixed-interval time-varying delays based on nonfragile feedback control to achieve the improved stability criterion. We also propose a new integral inequality with an exponential function to estimate the derivative of the Lyapunov–Krasovskii functional (LKF). Furthermore, the well-known Wirtinger’s inequality is a particular case of the new integral inequality. Using a toolbox optimization in MATLAB, we derive and solve new delay-dependent conditions in terms of linear matrix inequalities (LMIs). Additionally, we give three numerical examples to show the advantages of our obtained methods. The examples can apply the continuous time-varying delays that do not need to be differentiable. One of them presents the benchmark problem’s real-world application, which is a four-tank system.

This paper proposes improved Lyapunov-Krasovskii functionals (LKFs) for asymptotic stability of generalized neural networks (GNNs) with time-varying delays. By utilizing generalized free-weighting matrix inequality (GFWMI) and some mathematical techniques, sufficient conditions which are dependent on the size of time delays are derived for guaranteeing the stability of GNNs. Additionally, the augmented zero equality approach (AZEA) is applied to enhance the results and eliminate the free variables. Three numerical examples show that the proposed method can be effective and provide less conservative results than previous researches. [ABSTRACT FROM AUTHOR]

This article investigates new delay-dependent finite-time boundedness for generalized neural networks (GNNs) with mixed-interval time-varying delays based on nonfragile feedback control to achieve the improved stability criterion. We also propose a new integral inequality with an exponential function to estimate the derivative of the Lyapunov–Krasovskii functional (LKF). Furthermore, the well-known Wirtinger's inequality is a particular case of the new integral inequality. Using a toolbox optimization in MATLAB, we derive and solve new delay-dependent conditions in terms of linear matrix inequalities (LMIs). Additionally, we give three numerical examples to show the advantages of our obtained methods. The examples can apply the continuous time-varying delays that do not need to be differentiable. One of them presents the benchmark problem's real-world application, which is a four-tank system. [ABSTRACT FROM AUTHOR]

Abstract The problem of asymptotic stability and extended dissipativity analysis for the generalized neural networks with interval discrete and distributed time-varying delays is investigated. Based on a suitable Lyapunov–Krasovskii functional (LKF), an improved Wirtinger single integral inequality, a novel triple integral inequality, and convex combination technique, the new asymptotic stability and extended dissipativity criteria are achieved for the generalized neural networks with interval discrete and distributed time-varying delays. By the above methods, the less conservative asymptotic stability criteria are obtained for a special case of the generalized neural networks. By using the Matlab LMI toolbox, the derived new asymptotic stability and extended dissipativity criteria are expressed in terms of linear matrix inequalities (LMIs) that cover H ∞ $H_{\infty }$ , L 2 $L_{2}$ – L ∞ $L_{\infty }$ , passivity, and dissipativity performance by setting parameters in the general performance index. Finally, we show numerical examples which are less conservative than other examples in the literature. Moreover, we present numerical examples for asymptotic stability and extended dissipativity performance of the generalized neural networks, including a special case of the generalized neural networks.

This paper focuses on the asymptotic stability problems of the generalized neural networks (GNNs) with two additive time-varying delays (ATDs) and general activation function. First of all, a simple Lyapunov-Krasovskii functional (LKF) is established. Then not only the generalized free-weighting-matrix-based (GFWM-based) inequality together with its optimization strategy on choosing an arbitrary vector is utilized to estimate the single integral terms in derivative of the constructed LKF, but also the general activation function method is applied to introduce more information on cross terms of neuron activation function. Finally, a less conservative stability criterion together with its corollary is derived with convex combination technique, whose feasibility and superiority can be demonstrated with two numerical examples. [ABSTRACT FROM AUTHOR]

This paper focuses on the stability analysis of generalized neural networks with time-varying delays. First, a novel augmented Lyapunov-Krasovskii functional (LKF) is constructed by introducing a couple of integral vectors. Second, by utilizing the novel augmented LKF and a generalized free-weighting-matrix integral inequality, two further stability criteria are presented in this paper. Third, a less conservative stability condition by refining the allowable delay set is introduced. Finally, the four well-known numerical examples are given to demonstrate the effectiveness and improvements of the proposed methods.

The problem of asymptotic stability and extended dissipativity analysis for the generalized neural networks with interval discrete and distributed time-varying delays is investigated. Based on a suitable Lyapunov–Krasovskii functional (LKF), an improved Wirtinger single integral inequality, a novel triple integral inequality, and convex combination technique, the new asymptotic stability and extended dissipativity criteria are achieved for the generalized neural networks with interval discrete and distributed time-varying delays. By the above methods, the less conservative asymptotic stability criteria are obtained for a special case of the generalized neural networks. By using the Matlab LMI toolbox, the derived new asymptotic stability and extended dissipativity criteria are expressed in terms of linear matrix inequalities (LMIs) that cover H ∞ , L 2 – L ∞ , passivity, and dissipativity performance by setting parameters in the general performance index. Finally, we show numerical examples which are less conservative than other examples in the literature. Moreover, we present numerical examples for asymptotic stability and extended dissipativity performance of the generalized neural networks, including a special case of the generalized neural networks. [ABSTRACT FROM AUTHOR]

In this paper, the global robust asymptotic stability problem for a class of generalized reaction–diffusion uncertain stochastic neural networks with mixed delays is investigated under Dirichlet boundary conditions and Neumann boundary conditions, respectively. The proposed generalized neural networks model includes reaction–diffusion local field neural networks and reaction–diffusion static neural networks as its special cases. By using stochastic analysis approaches and constructing a suitable Lyapunov–Krasovskii functional, some simple and useful criteria for global robust asymptotic stability of the neural networks are obtained. According to the theoretical results, the influences of diffusion coefficients, diffusion spaces, stochastic perturbation, and uncertain parameters are analyzed. Finally, numerical examples are provided to show the feasibility and efficiency of the proposed methods, and by choosing different diffusion coefficients and diffusion spaces, different stability states can be achieved. [ABSTRACT FROM AUTHOR]

Abstract This study investigates the exponential stability and dissipativity issues for generalized neural networks with mixed time-varying delayed signals. The objective of the present work is to determine whether the new exponential stability and dissipativity criterions could be established for generalized delayed neural networks or not. A novel Lyapunov–Krasovskii functional that does not require one of terms that is positive definite is firstly constructed based on a peculiar structural matrix. It can be widely used to stability analyst, and better improve the algorithm performance. By employing novel integral inequalities and functional analysis theory, two optimization algorithms are developed. Finally, compared examples are presented to illustrate the effectiveness and the superiority of the proposed methods. [ABSTRACT FROM AUTHOR]

This paper researches the stability issue of generalized neural networks (GNN) with time-varying delay. For the delay, its derivative has an upper bound or is unknown. Firstly, the augmented Lyapunov-Krasovskii functional (LKF) is constructed based on the state vectors of the third order integral inequalities. Then, by introducing two sets of state vectors, the LKF derivative is presented as the quadratic and quintic polynomials of the delay, respectively. Next, the new quadratic and quintic polynomial negative definite conditions (NDCs) are proposed to set up the linear matrix inequalities (LMIs). In addition, based on the same LKF and third order integral inequalities, this paper proves that the introduction of extra state vectors increases the conservatism of the derived stability conditions. Eventually, the advantages of the provided conditions are illustrated by several numerical examples. • Based on the third order FMBIIs, the novel augmented LKF is constructed. • The LKF derivative is presented as the quadratic and quintic polynomials, respectively. • For the quadratic and quintic polynomials, the novel NDCs are provided. • This paper proves that the introduction of extra state vectors increases the conservativeness of the stability conditions. [ABSTRACT FROM AUTHOR]

The problem of non‐fragile extended dissipative control design for a class of generalized neural networks (GNNs) with interval time‐delay signals is investigated in this paper. By constructing a suitable Lyapunov‐Krasovskii functional (LKF) with double and triple integral terms, and estimating their derivative by using the Wirtinger single integral inequality (WSII) and Wirtinger double integral inequality (WDII) technique respectively, and that is mixed with the reciprocally convex combination (RCC) approach. A new delay‐dependent non‐fragile extended dissipative control design for GNNs are expressed in terms of the linear matrix inequalities (LMIs). Then, the desired non‐fragile extended dissipative controller can be obtained by solving the linear matrix inequalities (LMIs). Furthermore, a non‐fragile state feedback controller is designed for GNNs such that the closed‐loop system is extended dissiptive. Thus, the non‐fragile extended dissipative controller can be adopted to deal with the non‐fragile L2−L∞ performance, non‐fragile H∞ performance, non‐fragile passive performance, non‐fragile mixed H∞ and passivity performance, and non‐fragile dissipative performance for GNNs by selecting the weighting matrices. Finally, simulation studies are demonstrated for showing the feasibility of the proposed method. Among them, one example was supported by the real‐life application of the quadruple tank process system. [ABSTRACT FROM AUTHOR]

This paper deals with the problem of finding outer bound of forwards reachable sets and interbound of backwards reachable sets of generalized neural network systems with interval nondifferentiable time-varying delay and bounded disturbances. Based on constructing a suitable Lyapunov-Krasovskii functional and utilizing some improved Jensen integral-based inequalities, two sufficient conditions are derived for the existence of: (1) the smallest possible outer bound of forwards reachable sets and (2) the largest possible interbound of backwards reachable sets. These conditions are delay dependent and in the form of matrix inequalities, which therefore can be efficiently solved by using existing convex algorithms. Three numerical examples with simulation results are provided to demonstrate the effectiveness of our results. [ABSTRACT FROM AUTHOR]

This draft addresses the exponential stability problem for semi-Markovian jump generalized neural networks (S-MJGNNs) with interval time-varying delays. The exponential stability conditions are derived by establishing a suitable Lyapunov-Krasovskii functional and applying new analysis method. Improved results are obtained to guarantee the exponential stability of S-MJGNNs through improved reciprocally convex combination and new weighted integral inequality techniques. The method in this paper shows the advantages over some existing ones. To verify the advantages and benefits of employing proposed method is explained through numerical examples. [ABSTRACT FROM AUTHOR]

This paper focuses on the new criteria of stability analysis for generalized neural networks (GNNs) subject to time-varying delayed signals. A new methodology is employed with the aids of slack variables. By constructing an augmented Lyapunov–Krasovskii functional (LKF) involving Newton–Leibniz enumerating and triple integral term, some less conservative conditions are achieved in terms of linear matrix inequality (LMI). Numerical examples including real-time application are given to illustrate the superiority and effectiveness of proposed approach. [ABSTRACT FROM AUTHOR]

This paper deals with the problem of stability analysis for generalized delayed neural networks with interval time-varying delays based on the delay-partitioning approach. By constructing a suitable Lyapunov-Krasovskii functional with triple- and four-integral terms and using Jensen's inequality, Wirtinger-based single- and double-integral inequality technique and linear matrix inequalities (LMIs), which guarantees asymptotic stability of addressed neural networks. This LMI can be easily solved via convex optimization algorithm. The novelty of this paper is that the consideration of a new integral inequalities and Lyapunov-Krasovskii functional is shown to be less conservatism, and it takes fully the relationship between the terms in the Leibniz-Newton formula within the framework of LMIs. Moreover, it is assumed that the lower bound of the time-varying delay is not restricted to be zero. Finally, several interesting numerical examples are given to demonstrate the effectiveness and less conservativeness of our theoretical results over well-known examples existing in recent literature. [ABSTRACT FROM AUTHOR]

This paper explores the problem of synchronization of a class of generalized reaction-diffusion neural networks with mixed time-varying delays. The mixed time-varying delays under consideration comprise of both discrete and distributed delays. Due to the development and merits of digital controllers, sampled-data control is a natural choice to establish synchronization in continuous-time systems. Using a newly introduced integral inequality, less conservative synchronization criteria that assure the global asymptotic synchronization of the considered generalized reaction-diffusion neural network and mixed delays are established in terms of linear matrix inequalities (LMIs). The obtained easy-to-test LMI-based synchronization criteria depends on the delay bounds in addition to the reaction-diffusion terms, which is more practicable. Upon solving these LMIs by using Matlab LMI control toolbox, a desired sampled-data controller gain can be acuqired without any difficulty. Finally, numerical examples are exploited to express the validity of the derived LMI-based synchronization criteria. [ABSTRACT FROM AUTHOR]

This paper investigates the problems of exponential stability and dissipativity of generalized neural networks (GNNs) with time-varying delay signals. By constructing a novel Lyapunov–Krasovskii functionals (LKFs) with triple integral terms that contain more advantages of the state vectors of the neural networks, and the upper bound on the time-varying delay signals are formulated. We employ a new integral inequality technique (IIT), free-matrix-based (FMB) integral inequality approach, and Wirtinger double integral inequality (WDII) technique together with the reciprocally convex combination (RCC) approach to bound the time derivative of the LKFs. An improved exponential stability and strictly ( Q , S , R ) - γ -dissipative conditions of the addressed systems are represented by the linear matrix inequalities (LMIs). Finally, four interesting numerical examples are developed to verify the usefulness of the proposed method with a practical application to a biological network. [ABSTRACT FROM AUTHOR]

This paper deals with the problem of stability analysis of generalized neural networks with time delays. It should be noted that additive time-varying delays are taken in the state of the neural networks. A novel augmented Lyapunov–Krasovskii (L–K) functional which involves more information on the activation function of the neural networks and upper bound of the additive time-varying delays is constructed. By introducing some zero equations and using the reciprocal convex combination technique and Finsler׳s lemma, an improved delay-dependent stability criterion is derived in terms of linear matrix inequalities (LMIs), which can be efficiently solved via standard numerical software. Finally, three numerical examples are provided to demonstrate the less conservatism and effectiveness of the proposed results. [ABSTRACT FROM AUTHOR]

This paper examined for the first time the challenge of unified dissipativity state estimation of delayed generalized impulsive neural networks (GINNs) with leaky delay effects. To estimate the upper bounds of the Lyapunov Krasovskii functionals (LKFs), the tighter integral inequality (TII) and reciprocally convex inequality (RCI) approaches are employed, and certain criteria are provided in the form of linear matrix inequalities (LMIs). As a response, a new delayed-dependent criterion for establishing whether the estimated error network is unified dissipative is developed. By modifying the values of the suitable matrices, the notion of a unified dissipativity-based estimating state may be used to find the multi-dynamic state estimation of GINNs. The recommended technique's benefit is displayed by multiple numerical examples, one of which was sponsored by a practical implementation of the benchmark problem (i.e., the quadruple-tank process system (QTPS)) that is involved with reasonable issues, particularly the impulse impacts in the sense of a unified dissipativity performance. [ABSTRACT FROM AUTHOR]

Abstract: This paper is concerned with global asymptotic stability for a class of generalized neural networks with interval time-varying delays by constructing a new Lyapunov–Krasovskii functional which includes some integral terms in the form of . Some useful integral inequalities are established for the derivatives of those integral terms introduced in the Lyapunov–Krasovskii functional. A matrix-based quadratic convex approach is introduced to prove not only the negative definiteness of the derivative of the Lyapunov–Krasovskii functional, but also the positive definiteness of the Lyapunov–Krasovskii functional. Some novel stability criteria are formulated in two cases, respectively, where the time-varying delay is continuous uniformly bounded and where the time-varying delay is differentiable uniformly bounded with its time-derivative bounded by constant lower and upper bounds. These criteria are applicable to both static neural networks and local field neural networks. The effectiveness of the proposed method is demonstrated by two numerical examples. [Copyright &y& Elsevier]

Abstract: This paper investigates the synchronization problem of generalized stochastic neural networks with mixed time-varying delays and reaction-diffusion terms using linear feedback control. Lyapunov stability theory combining with stochastic analysis approaches is employed to derive sufficient criteria ensuring the coupled chaotic generalized stochastic neural networks to be globally exponentially synchronized. The generalized neural networks model considered includes reaction-diffusion Hopfield neural networks, reaction-diffusion bidirectional associative memory neural networks, and reaction-diffusion cellular neural networks as its special cases. It is theoretically proven that these synchronization criteria are more effective than some existing ones. This paper also presents some illustrative examples and uses simulated results of these examples to show the feasibility and effectiveness of the proposed scheme. [Copyright &y& Elsevier]

This paper is concerned with global asymptotic stability for a class of generalized neural networks (NNs) with interval time-varying delays, which include two classes of fundamental NNs, i.e., static neural networks (SNNs) and local field neural networks (LFNNs), as their special cases. Some novel delay-independent and delay-dependent stability criteria are derived. These stability criteria are applicable not only to SNNs but also to LFNNs. It is theoretically proven that these stability criteria are more effective than some existing ones either for SNNs or for LFNNs, which is confirmed by some numerical examples. [ABSTRACT FROM AUTHOR]

Abstract: The paper is concerned with robust stability for generalized neural networks (GNNs) with both interval time-varying delay and time-varying distributed delay. Through partitioning the time-delay, choosing one augmented Lyapunov–Krasovskii functional, employing free-weighting matrix method and convex combination, the sufficient conditions are obtained to guarantee the robust stability of the concerned systems. These stability criteria are presented in terms of linear matrix inequalities (LMIs) and can be easily checked. Finally, three numerical examples are given to demonstrate the effectiveness and reduced conservatism of the obtained results. [Copyright &y& Elsevier]

Abstract: Using the Lyapunov–Krasovskii functional method and the linear matrix inequality (LMI) technique, this paper is concerned with the robust stability of generalized neural networks with multiple discrete delays and multiple distributed delays. The global stability of the equilibrium point is proved under mild conditions, where the activation function is neither differentiable nor strictly monotone. For the considered system, a novel robust stability criterion of the system is derived, which can be easily solved by efficient convex optimization algorithms. And two numerical examples are given to justify the obtained results. [Copyright &y& Elsevier]

Abstract: In this paper, we essentially drop the requirement of Lipschitz condition on the activation functions. Only using physical parameters of neural networks, some new criteria concerning global exponential stability for a class of generalized neural networks with time-varying delays are obtained. The neural network model considered includes the delayed Hopfield neural networks, bidirectional associative memory networks, and delayed cellular neural networks as its special cases. Since these new criteria do not require the activation functions to be differentiable, bounded or monotone nondecreasing, the connection weight matrices to be symmetric and the delay function to be differentiable, our results are mild and more general than previously known criteria. Four illustrative examples are given to demonstrate the effectiveness of the obtained results. [Copyright &y& Elsevier]

By employing several Lyapunov functionals, the global exponential stability and asymptotic stability of generalized neural networks with distributed delays are investigated in this paper. A number of sufficient conditions for these types of stability are derived. They are milder and more general than previously known criteria, and can be applied to neural networks with constant connection weights as well as a broad range of activation functions assuming neither differentiability nor strict monotonicity. Furthermore, the results obtained for generalized neural networks with distributed delays do not assume symmetry of the connection matrix. [Copyright &y& Elsevier]