Search

This paper investigates the stability of complex-valued neural networks (CVNNs) with semi-Markovian jump (sMJ) and generally uncertain transition rates. Each transition rate may be totally unknown or its estimate is determined. Firstly, two improved reciprocally convex inequalities (RCIs) and three less conservative integral inequalities are generalized to the complex-valued domain. Secondly, the existence and uniqueness of the addressed networks are proposed by the complex-valued homeomorphism theorem. Thirdly, by constructing a Lyapunov–Krasovskii functional (LKF), delay-dependent robust stability criteria of the CVNNs are obtained by utilizing the improved complex-valued RCIs and integral inequalities. Finally, simulations are presented to demonstrate the effectivenes and practicality of the established method. [ABSTRACT FROM AUTHOR]

This paper investigates the synchronization of complex dynamic networks with time-varying delay and general semi-Markovian jump. The general transition rates include completely unknown and uncertain but bounded as two special cases. First, by introducing auxiliary vectors with a few nonorthogonal polynomials, two free-matrix-based integral inequalities are developed, which encompass some existing ones as special cases. Second, an integral- based delay-product-type Lyapunov-Krasovskii functional is constructed, which fully considers the information of time delay. By utilizing a deley-dependent controller, two sufficient conditions are derived to realize the global stochastic mean-square synchronization by employing the established inequalities to evaluate the infinitesimal generator of the functional. This paper takes all possibilities into consideration and divides the general transition rates into five cases, which is never investigated before. Finally a numerical example is given to show the effectiveness and practicality of the presented method. [ABSTRACT FROM AUTHOR]

This paper discusses the stochastic stability for genetic regulatory networks (GRNs) with semi-Markov switching and time-varying delays where the transition rates (TRs) of the modes are partially unknown. By proposing vectors with three Legendre polynomials and three weighted Legendre polynomials, two free-matrix-based integral inequalities are derived, which involves several existing ones as their special cases. Then, two appropriate Lyapunov–Krasovskii functionals (LKFs) are established to be apt for the acquired inequalities. By introducing some free-weight matrices and utilizing the acquired integral inequalities, new sufficient conditions are proposed to ensure the stochastically asymptotic stability of analyzed networks in the mean-square sense. Finally, two simulation examples are put forward to show the effectiveness and less conservatism of the presented criteria. [ABSTRACT FROM AUTHOR]

This paper investigates the event-triggered synchronization of complex dynamic networks (CDNs) with semi-Markov switching and time-varying delay. First, by proposing auxiliary vectors with a few nonorthogonal polynomials, two slack-matrix-based integral inequalities are formulated, which encompass some existing ones as special cases. Second, a triple-integral-based delay-product-type (TIDPT) Lyapunov-Krasovskii functional (LKF) is formulated, which fully utilizes the information of time delay. After designing a controller via the event- triggered scheme, some sufficient conditions are proposed to achieve the global stochastic synchronization by utilizing the reciprocally convex matrix inequality (RCMI) and the founded inequalities to evaluate the derivative of the established LKF. A numerical example is employed to show the effectiveness and practicability of the proposed method. [ABSTRACT FROM AUTHOR]

This paper probes into the synchronization for memristor-based hybrid neural networks via nonlinear coupling. At first, a new condition is established to judge whether quadratic functions are negative or not on a closed interval regardless of their concavity or convexity. Then, by utilizing Legendre orthogonal polynomials, a recent extended integral inequality with free matrices is popularized to get tighter lower bound of some integral terms. Next, based on a novel Lyapunov functional, by applying our new integral inequality with free matrices, linear convex combination method and the new criterion, a new delay-dependent condition is gained to reach the global synchronization for the considered neural networks. At last, an example is presented to account for the validity of our results. [ABSTRACT FROM AUTHOR]

This paper probes into the synchronization of delayed competitive memristor-based neural networks (CMNNs). Firstly, a new loosened integral inequality is advanced to decrease the estimation difference of auxiliary function-based integral inequalities (AFBIs). Next, by utilizing Legendre polynomials and appropriate loose variables, a delay-product function (DPF) is advanced to employ extra freedom and more information on system states. Then, by proposing nonlinear controller and Lyapunov-Krasovskii functional (LKF) based on above DPF, two delay-dependent principles are offered to accomplish the global synchronization by making use of Chen et al.'s integral inequalities and quadratic combination technique. Finally, an example is supplied to reveal the effectiveness of the presented results. [ABSTRACT FROM AUTHOR]

This paper inquires into the synchronization for delayed chaotic memristive neural networks. First, a novel criterion is proposed to determine whether a quadratic function is negative or not on a closed interval without regard for its convexity or concavity. Then, a novel Lyapunov functional is established which is based on Chen et al.'s integral inequalities. Next, by applying Moon et al.'s inequality, Chen et al.'s integral inequalities, linear convex combination technique and the novel criterion, two novel delay-dependent criteria are presented to realize the global asymptotical synchronization for the chaotic memristive neural networks. Finally, an example is given out to explain the effectiveness of the theoretical results. [ABSTRACT FROM AUTHOR]

This paper focuses on the stochastic synchronization problem for a class of fuzzy Markovian hybrid neural networks with random coupling strengths and mode-dependent mixed time delays in the mean square. First, a novel free-matrix-based single integral inequality and two novel free-matrix-based double integral inequalities are established. Next, by employing a novel augmented Lyapunov–Krasovskii functional with several mode-dependent matrices, applying the theory of Kronecker product of matrices, Barbalat's Lemma and the new free-matrix-based integral inequalities, two delay-dependent conditions are established to achieve the globally stochastic synchronization for the mode-dependent fuzzy hybrid coupled neural networks. Finally, two numerical examples with simulation are provided to illustrate the effectiveness of the presented criteria. [ABSTRACT FROM AUTHOR]

This paper investigates the globally asymptotic synchronization for hybrid neural networks with random coupling strengths and mixed time-delays in the mean square. By employing a novel augmented Lyapunov–Krasovskii functional (LKF), applying the theory of Kronecker product of matrices, Barbalat’s Lemma and the auxiliary function-based integral inequalities, several novel delay-dependent conditions are established to achieve the globally stochastic synchronization for the hybrid coupled neural networks. Two presented criteria do not require all the symmetric matrices involved in the employed quadratic LKF to be positive definite. Furthermore, the conservatism of delay-dependent stability conditions can be reduced due to the relaxation on the positive-definiteness of some Lyapunov matrices. Finally, two numerical examples with simulation are provided to illustrate the effectiveness of the presented criteria. [ABSTRACT FROM AUTHOR]

This paper investigates the problem of stability of fuzzy neural networks with time-varying and continuously distributed delays under impulsive perturbations. Two new delay-dependent criteria are obtained in terms of linear convex combination technique, the reciprocal convex lemma, Wirtinger-based integral inequality, and the quadratic convex combination method. The first presented criterion does not require all the symmetric matrices involved in the employed quadratic Lyapunov–Krasovskii functional to be positive definite. Furthermore, the conservatism of delay-dependent stability conditions can be reduced due to the relaxation on the positive-definiteness of some Lyapunov matrices. It is shown numerically that the stability criteria proposed in this paper are less conservative than some of the latest results in the literature. [ABSTRACT FROM AUTHOR]

The stability is investigated for a kind of fuzzy cellular neural networks with time-varying and continuously distributed delays under impulsive perturbations. When the Wirtinger-based integral inequality is applied to partitioned integral terms in the derivation of matrix inequality conditions, a new kind of linear combination of positive functions emerges weighted by the inverses of cubic convex parameters. This paper proposes an efficient method called third-order reciprocally convex approach to manipulate such a combination by extending the reciprocal convex technique. By utilizing Briat lemma and reciprocal convex approach, this paper derives several novel sufficient conditions to ensure the global asymptotic stability of the equilibrium point of the considered networks. Based on the derived criteria, a lower-bound estimation can be obtained of the largest stability interval for a class of fuzzy cellular neural networks under impulsive perturbations. Simulation examples demonstrate that the presented method can significantly reduce the conservatism of the existing results, and lead to wider applications. [ABSTRACT FROM AUTHOR]

This paper investigates the synchronization problem for a class of chaotic neural networks with discrete and unbounded distributed time delays under stochastic perturbations. Firstly, based on the Wirtinger-based double integral inequality, two novel inequalities are proposed, which are multiple integral forms of the Wirtinger-based integral inequality. Next, by applying the Jensen-type integral inequality for stochastic case and combining the Jensen integral inequality with the reciprocally convex combination approach, a delay-dependent criterion is developed to achieve the synchronization for the stochastic chaotic neural networks in the sense of mean square. In the case of no stochastic perturbations, by applying the reciprocally convex combination approach for high order case and a free-matrix-based inequality, novel delay-dependent conditions are established to achieve the synchronization for the chaotic neural networks. All the results are based on dividing the bounding of activation function into two subintervals with equal length. Finally, two numerical examples are provided to demonstrate the effectiveness of the theoretical results. [ABSTRACT FROM AUTHOR]

This paper investigates the synchronization problem for chaotic memristor-based neural networks with time-varying delays. First, a novel lemma is proposed to deal with the switching jump parameters. Then, a novel inequality is established which is a multiple integral form of the Wirtinger-based integral inequality. Next, by applying the reciprocally convex combination approach, linear convex combination technique, auxiliary function-based integral inequalities and a free-matrix-based inequality, several novel delay-dependent conditions are established to achieve the globally asymptotical synchronization for the chaotic memristor-based neural networks. Finally, a numerical example is provided to demonstrate the effectiveness of the theoretical results. [ABSTRACT FROM AUTHOR]

This paper investigates the global asymptotic stability of fuzzy neural networks with time-varying and unbounded continuously distributed delays in mean square. Based on a new Lyapunov-Krasovskii functional, by effective combination of Jensen integral inequality with reciprocally convex and quadratic convex combination method, several novel sufficient conditions are derived to ensure the global asymptotic stability of the equilibrium point of the considered networks in mean square. The proposed results, which are expressed in terms of linear matrix inequalities, can be easily verified via MATLAB software. The main advantage of the proposed criteria lies in its reduced conservatism by means of the time delay-decomposition technique and Wirtinger-based inequality. In addition to that, a numerical example is given to demonstrate the effectiveness and less conservativeness of our theoretical results over the existing literature. [ABSTRACT FROM AUTHOR]

A robust adaptive feedback controller is designed to achieve complete synchronization of a class of neutral-type stochastic Markovian jump neural networks with mode-dependent and mixed delays. The mixed delays consist of time-varying discrete delays and continuously distributed delays. By employing Wirtinger-based integral inequality, a reciprocally convex combination technique and a generalized LaSalle-type invariance principle for stochastic Markovian differential delay equations, this paper establishes two globally almost surely asymptotical stability conditions of the error dynamical system in the mean-square sense for all admissible uncertainties. An example and its numerical simulation are given to demonstrate the effectiveness of the theoretical results. [ABSTRACT FROM AUTHOR]

This paper investigates the stability of switched Hopfield neural networks of neutral type with time-varying delay and continuously distributed delay. By using the quadratic convex combination method, the reciprocal convex combination approach, some generalized Jensen integral inequalities, and the free-weight matrix method, several novel sufficient conditions are derived to ensure the asymptotic stability of the equilibrium point of the considered networks. The proposed results, which do not require the differentiability of the activation functions, can be easily checked via Matlab software. Finally, three numerical examples are given to demonstrate the effectiveness and less conservativeness of our theoretical results over existing literature. [ABSTRACT FROM AUTHOR]

The robust stochastic convergence and stability in mean square are investigated for a class of uncertain neutral-type neural networks with both Markovian jump parameters and mixed delays. First, by employing the Lyapunov method and a generalized Halanay-type inequality for stochastic differential equations, a delay-dependent condition is derived to guarantee the state variables of the discussed neural networks to be globally uniformly exponentially stochastic convergent to a ball in the state space with a prespecified convergence rate. Next, by applying the Jensen integral inequality and a novel reciprocal convex lemma, a delay-dependent criterion is developed to achieve the globally robust stochastic stability in mean square. With some parameters being fixed in advance, the proposed conditions are all expressed in terms of LMIs, which can be solved numerically by employing the standard MATLAB LMI toolbox package. Finally, two illustrated examples are given to show the effectiveness and less conservatism of the obtained results over some existing works. Copyright © 2014 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

This paper studies the globally asymptotic stability of neutral-type impulsive neural networks with discrete and bounded continuously distributed delays. By using the Lyapunov functional method, quadratic convex combination approach, a novel Gu's Lemma, Jensen integral inequality and linear convex combination technique, several novel sufficient conditions are derived to ensure the globally asymptotic stability of the equilibrium point of the networks. The proposed results, which do not require the differentiability and monotonicity of the activation functions, can be easily checked via Matlab software. Finally, two numerical examples are given to demonstrate the effectiveness of our theoretical results. [ABSTRACT FROM AUTHOR]

The anti-synchronization control is investigated for a class of uncertain stochastic chaotic neural networks with both Markovian jump parameters and mixed delays. The mixed delays consists of discrete and distributed time-varying delays. First, by combining the Lyapunov method and a generalized Halanay-type inequality for stochastic differential equations, a delay-dependent criterion is established to guarantee the state variables of the discussed stochastic chaotic neural networks to be globally exponential anti-synchronized. Next, by utilizing a novel lemma and the Jensen integral inequality, a delay-dependent criterion is proposed to achieve the globally stochastic robust anti-synchronization. With some parameters being fixed in advance, the proposed conditions are all expressed in terms of linear matrix inequalities, which can be solved numerically by employing the standard Matlab LMI toolbox package. Finally, two examples are proposed to demonstrate the effectiveness and usefulness of the proposed results. [ABSTRACT FROM AUTHOR]

This paper studies the exponential synchronization problem for a class of stochastic perturbed chaotic neural networks with both Markovian jump parameters and mixed time delays. The mixed delays consist of discrete and distributed time-varying delays. At first, based on a Halanay-type inequality for stochastic differential equations, by virtue of drive-response concept and time-delay feedback control techniques, a delay-dependent sufficient condition is proposed to guarantee the exponential synchronization of two identical Markovian jumping chaotic-delayed neural networks with stochastic perturbation. Then, by utilizing the Jensen integral inequality and a novel Lemma, another delay-dependent criterion is established to achieve the globally stochastic robust synchronization. With some parameters being fixed in advance, these conditions can be solved numerically by employing the Matlab software. Finally, a numerical example with their simulations is provided to illustrate the effectiveness of the presented synchronization scheme. [ABSTRACT FROM AUTHOR]

This paper investigates the global asymptotic stability of a kind of fuzzy cellular neural networks with mixed delays under impulsive perturbations. The mixed delays include constant delay in the leakage term (i.e., 'leakage delay'), time-varying delays, and continuously distributed delays. By using the quadratic convex combination method, reciprocal convex approach, Jensen integral inequality, and linear convex combination technique, several novel sufficient conditions are derived to ensure the global asymptotic stability of the equilibrium point of the considered networks. The proposed results, which do not require the differentiability and monotonicity of the activation functions, can be easily checked via Matlab software. Finally, two numerical examples are given to demonstrate the effectiveness and less conservativeness of our theoretical results over existing literature. [ABSTRACT FROM AUTHOR]

Abstract: This paper investigates a class of mixed recurrent neural networks with time delay in the leakage term under impulsive perturbations. The mixed time-delays consist of both discrete and distributed delays. By using the Lyapunov functional method, linear matrix inequality approach and general convex combination technique, two novel sufficient conditions are derived to ensure the global asymptotic stability of the equilibrium point of the networks. The proposed results, which do not require the boundedness, differentiability and monotonicity of the activation functions, can be easily checked via Matlab software. Moreover, they indicate that the stability behavior of neural networks is very sensitive to the time delay in the leakage term. Finally, numerical examples are given to demonstrate the effectiveness of our theoretical results. [Copyright &y& Elsevier]

Abstract: This paper introduces an effective approach to studying the passivity of neutral-type neural networks with discrete and continuous distributed time-varying delays. By employing a novel Lyapunov–Krasovskii functional based on delay partitioning, several improved delay-dependent passivity conditions are established to guarantee the passivity of uncertain neural networks by applying the Jensen integral inequality. These criteria are expressed in the framework of linear matrix inequalities, which can be verified easily by means of standard Matlab software. One special case of the obtained criteria turns out to be equivalent to some existing result with same reduced conservatism but including fewer slack variables. As the present passivity conditions involve fewer free-weighting matrices, the computational burden is largely reduced. Three examples are provided to demonstrate the advantage of the theoretical results. [Copyright &y& Elsevier]

Novel passivity criteria are presented for the passivity of a class of cellular neural networks with discrete and unbounded distributed time-varying delays. Two types of uncertainty are considered: one is time-varying structured uncertainty while the other is interval uncertainty. The Gu's discretized Lyapunov–Krasovskii functional method is integrated with the technique of introducing the free-weighting matrix between the terms of the Leibniz–Newton formula. The integrated method leads to the establishment of new delay-dependent sufficient conditions in form of linear matrix inequalities for passivity of delayed neural networks. A numerical simulation study is conducted to demonstrate the obtained theoretical results, which shows their less conservatism than the existing passivity criteria. [ABSTRACT FROM AUTHOR]

SUMMARY The exponential stability problem is investigated for a class of uncertain stochastic neural networks with discrete and unbounded distributed time delays. Two types of uncertainty are considered: one is time-varying structured uncertainty, whereas the other is interval uncertainty. With the application of the Jensen integral inequality and constructing appropriate Lyapunov-Krasovskii functional based on delay partitioning, several improved delay-dependent criteria are developed to achieve the exponential stability in mean square in terms of linear matrix inequalities. It is established theoretically that two special cases of the obtained criteria are less conservative than some existing results but including fewer slack variables. As the present conditions involve fewer free weighting matrices, the computational burden is largely reduced. Three numerical examples are provided to demonstrate the effectiveness of the theoretical results. Copyright © 2012 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

This paper studies the existence, uniqueness and globally robust exponential stability for a class of uncertain neutral-type Cohen–Grossberg neural networks with time-varying and unbounded distributed delays. Based on Lyapunov–Krasovskii functional, by involving a free-weighting matrix, using the homeomorphism mapping principle, Cauchy–Schwarz inequality, Jensen integral inequality, linear matrix inequality techniques and matrix decomposition method, several delay-dependent and delay-independent sufficient conditions are obtained for the robust exponential stability of considered neural networks. Two numerical examples are given to show the effectiveness of our results. [ABSTRACT FROM PUBLISHER]

The global exponential stability is analyzed for a class of high-order Hopfield-type neural networks with time-varying delays. Based on the Lyapunov stability theory, together with the linear matrix inequality approach and free-weighting matrix method, some less conservative delay-independent and delay-dependent sufficient conditions are presented for the global exponential stability of the equilibrium point of the considered neural networks. Two numerical examples are provided to demonstrate the effectiveness of the proposed stability criteria. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, the state estimation problem is investigated for neural networks with time-varying delays as well as general activation functions. By applying the Finsler''s Lemma and constructing appropriate Lyapunov–Krasovskii functional based on delay partitioning, several improved delay-dependent conditions are developed to estimate the neuron state with some available output measurements such that the error-state system is global asymptotically stable. It is established theoretically that one special case of the obtained criteria is equivalent to some existing result with same conservatism but including fewer LMI variables. As the present conditions involve no free-weighting matrices, the computational burden is largely reduced. Two examples are provided to demonstrate the effectiveness of the theoretical results. [Copyright &y& Elsevier]

Abstract: The problem of global asymptotic stability analysis is studied for a class of cellular neural networks with time-varying delay. By defining a Lyapunov–Krasovskii functional, a new delay-dependent stability condition is derived in terms of linear matrix inequalities. The obtained criterion is less conservative than some previous literature because free-weighting matrix method and the Jensen integral inequality are considered. Three illustrative examples are given to demonstrate the effectiveness of the proposed results. [Copyright &y& Elsevier]

Abstract: The problem ensuring the global robust exponential stability of a class of delayed cellular neural networks with norm-bounded uncertainties is studied. Without assuming the boundedness of the activation functions, by applying the idea of vector Lyapunov function and linear matrix inequality (LMI) techniques, some sufficient conditions for the global robust exponential stability of uncertain cellular neural networks and the existence, uniqueness, global exponential stability of cellular neural networks are obtained, which generalize the previous results in the literature. The criteria are easy to be verified, since they take the form of LMI. Three illustrative examples are given to demonstrate the effectiveness of the proposed results. [Copyright &y& Elsevier]

Cubic Hermite–Pade´ approximation to the exponential function with coefficient polynomials of degree at most m is considered. Explicit formulas are obtained for the coefficient polynomials. An exact asymptotic expression is obtained for the error function and it is also shown that these generalized Pade´-type approximations can be used to asymptotically minimize the expressions on the unit disk. [Copyright &y& Elsevier]