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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 studies the leader-following event-triggered consensus of multi-agent systems with nonlinear dynamics and semi-Markov jump. The information on transition rates is incompletely known. First, by applying weighted orthogonal polynomials, two new integral inequalities are established, which include some existing ones. Second, an event-triggered scheme is presented to save the precious communication resources. After constructing an augmented Lyapunov–Krasovskii functional, a few sufficient conditions are derived to achieve the leader-following event-triggered consensus by utilizing the presented inequalities to manipulate the derivative of the functional. Finally, numerical simulation shows the effectiveness of the proposed 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 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 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]

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]