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This paper investigates the event-triggered impulsive synchronization of a variable-order fractional chaotic Lur'e system with the application of fractal interpolation based image encryption. The variable-order fractional Lur'e system is modeled into fractional order Chua's circuit model with short memory. The synchronization is achieved using event-triggered impulsive control and short memory for chaotic Lur'e systems, employing linear matrix inequalities. The variable-order fractional Chua's circuit systems successfully accomplish their synchronization using both impulsive and event-triggered impulsive control. Furthermore, fractal interpolation function (with function scalings) is applied to reconstruct the chaotic attractors. The Riemann-Liouville variable-order fractional calculus of diverse fractal functions is also investigated in connection with the study on variable-order fractional systems. The interpolated sequence, along with the Arnold transform, modified Fisher Yates algorithm, and additive diffusion, is utilized to propose an image encryption algorithm. Various statistical analyses are conducted to assess the effectiveness of the proposed algorithm. [ABSTRACT FROM AUTHOR]

The Nilgiris biosphere reserve in the Western Ghats of South India is an International Biosphere Reserve. This paper focuses on the diversity of woody species found in the Nilgiri Hills’ evergreen forest. A total of 133 plant species have been identified and their quantitative features such as density, frequency, relative density, relative frequency, basal area and their absolute values were obtained. The specific purpose for plant species identification in the Nilgiri Biosphere reserve is to understand the plant vegetation characteristics, to estimate the species richness and also to identify the endemic, vulnerable and threatened species so that they can be conserved in the future. In this paper, we select the best soil type for cultivation and identify the most endemic species in the Nilgiris biosphere reserve which involves multiple criteria leading to a multi criteria decision making problem. In order to arrive to this result, we propose the notion of interval type 2 q-rung orthopair fuzzy sets in terms of trapezoidal numbers which will effectively reflect the ambiguity in these real-life circumstances. We also describe the concept of interval type 2 q-rung orthopair fuzzy sets and its implications in the scenario under discussion. Some of its properties are also discussed together with the interval type 2 q-rung orthopair Bonferroni mean operator and interval type 2 q-rung orthopair normalised weighted Bonferroni mean operator that are proposed. In order to demonstrate the efficiency of the operator and to validate it, we also compared our results with those of the existing operators. [ABSTRACT FROM AUTHOR]

In this study, we investigate the problem of multiple Mittag-Leffler stability analysis for fractional-order quaternion-valued neural networks (QVNNs) with impulses. Using the geometrical properties of activation functions and the Lipschitz condition, the existence of the equilibrium points is analyzed. In addition, the global Mittag-Leffler stability of multiple equilibrium points for the impulsive fractional-order QVNNs is investigated by employing the Lyapunov direct method. Finally, simulation is performed to illustrate the effectiveness and validity of the main results obtained. [ABSTRACT FROM AUTHOR]

This paper deals with the impulsive synchronization problem for a class of inertial memristor-based neural networks (IMNNs) with time delays by applying average impulsive interval approach. By adopting proper variable transformation, the original system can be converted into first-order differential equations. By utilizing Lyapunov theory, theory of differential inclusion, Halanay inequality and average impulsive interval approach, we attain some adequate conditions that make sure the exponential synchronization of IMNNs under the impulsive control technique. Moreover some delay-dependent conditions for delayed impulsive synchronization of the considered system is obtained. Finally, numerical simulations are offered to exhibit the capacity of our theoretical findings. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the problem of stability and synchronization of fractional-order complex-valued neural networks with time delay. By using Lyapunov-Krasovskii functional approach, some linear matrix inequality (LMI) conditions are proposed to ensure that the equilibrium point of the addressed neural networks is globally Mittag-Leffler stable. Moreover, some sufficient conditions for projective synchronization of considered fractional-order complex-valued neural networks are derived in terms of LMIs. Finally, two numerical examples are given to demonstrate the effectiveness of our theoretical results. [ABSTRACT FROM AUTHOR]

This study is concerned with the exponential $$H_{\infty }$$ synchronization criteria for complex dynamical networks of Lur'e- type systems with non-delay and delay couplings as well as external disturbances. The pinning sampled-data control is designed to achieve synchronization, in which only the selection of nodes is controlled, instead of the whole network. By constructing an improved Lyapunov-Krasovskii functional and utilizing the reciprocal convex method, the sufficient conditions are expressed in terms of linear matrix inequalities to ensure synchronization of the proposed network with a guaranteed $$H_{\infty }$$ performance. Different from most existing studies, the addressed synchronization criteria depend not only on the upper bounds of the sampling intervals but also on the lower bounds; therefore, potentially leading to reduced conservative criteria. The desired control gain matrices are calculated by solving the obtained linear matrix inequalities that guarantee the exponential stability of the error system under the $$H_{\infty }$$ norm. Finally, the effectiveness of the proposed method is demonstrated through numerical simulations. [ABSTRACT FROM AUTHOR]

This paper considers a class of fractional-order complex-valued Hopfield neural networks (CVHNNs) with time delay for analyzing the dynamic behaviors such as local asymptotic stability and Hopf bifurcation. In the case of a neural network with hub and ring structure, the stability of the equilibrium state is investigated by analyzing the eigenvalue of the corresponding characteristic matrix for the hub and ring structured fractional-order time delay models using a Laplace transformation for the Caputo-fractional derivatives. Some sufficient conditions are established to guarantee the uniqueness of the equilibrium point. In addition, conditions for the occurrence of a Hopf bifurcation are also presented. Finally, numerical examples are given to demonstrate the effectiveness of the derived results. [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 focuses on the exponential synchronization of nonlinearly coupled Markovian jumping complex dynamical networks with stochastic perturbations under delayed impulsive controller. The Markovian jumping parameters are represented as a continuous-time, finite-state Markov chain. The impulsive control law is defined with both distributed as well as discrete time-varying delays. By designing the efficient impulsive control strategy and by using the Lyapunov method and Ito's formula, some simple and easily realized adequate conditions that assure the exponential synchronization of considered complex dynamical networks are derived in mean square sense. Finally, some simulation results are granted to display the effects of the theoretical findings. [ABSTRACT FROM AUTHOR]

This paper is devoted to investigate the problem of global asymptotic synchronization of an array of N randomly coupled reaction-diffusion neural networks with Markovian jumping parameters and mixed delays using sampled-data control technique. The jump parameters are determined by a continuous-time, discrete-state Markovian chain, and the mixed time delays under consideration comprise both discrete and distributed delays. A multiple integral inequality is proposed firstly in Markovian jump reaction-diffusion neural networks with mixed delays. Through constructing appropriate Lyapunov-Krasovskii functional including multiple integral terms, some novel synchronization criteria in terms of linear matrix inequalities are derived. The obtained LMIs can be easily verified for feasibility through any of the available softwares. Finally, numerical examples with simulations are provided to illustrate the effectiveness of the proposed theoretical results. [ABSTRACT FROM AUTHOR]

This paper is concerned with the problem of stability and pinning synchronization of a class of inertial memristive neural networks with time delay. In contrast to general inertial neural networks, inertial memristive neural networks is applied to exhibit the synchronization and stability behaviors due to the physical properties of memristors and the differential inclusion theory. By choosing an appropriate variable transmission, the original system can be transformed into first order differential equations. Then, several sufficient conditions for the stability of inertial memristive neural networks by using matrix measure and Halanay inequality are derived. These obtained criteria are capable of reducing computational burden in the theoretical part. In addition, the evaluation is done on pinning synchronization for an array of linearly coupled inertial memristive neural networks, to derive the condition using matrix measure strategy. Finally, the two numerical simulations are presented to show the effectiveness of acquired theoretical results. [ABSTRACT FROM AUTHOR]

This study deals with the problem of exponential synchronization and state estimation for singularly perturbed complex networks (SPCNs) with coupling delay under sampled-data control technique. Every node of the SPCNs involve both 'fast' and 'slow' dynamics that reveals the singular perturbation behavior. By constructing novel Lyapunov functional and by using Kronecker product, some adequate conditions which assure the exponential synchronization are attained in the form of linear matrix inequalities. Moreover, the exponential state estimation problem for the SPCNs are also considered and the state estimator is designed. Lastly, numerical simulations are presented to validate the advantage of the propound theoretical results. [ABSTRACT FROM AUTHOR]

Memristor is the new model two-terminal nonlinear circuit device in electronic circuit theory. This paper deals with the problem of global dissipativity and global exponential dissipativity for memristor-based complex-valued neural networks (MCVNNs) with time-varying delays. Sufficient global dissipativity conditions are derived from the theory of M-matrix analysis, and the globally attractive set as well as the positive invariant set is established. By constructing Lyapunov-Krasovskii functionals and using a linear matrix inequality technique, some new sufficient conditions on global dissipativity and global exponential dissipativity of MCVNNs are derived. Finally, two numerical examples are presented to demonstrate the effectiveness of our proposed theoretical results. [ABSTRACT FROM AUTHOR]

This paper deals with the problem of robust $$H_{\infty }$$ synchronization of chaotic Lur'e systems with time-varying delays via sampled-data control. In order to make full use of the information about sampling intervals, nonlinear functions and time-varying delays, an improved Lyapunov-Krasovskii (L-K) functional is introduced. Based on reciprocal convex combination technique, sufficient conditions are derived in terms of linear matrix inequalities (LMIs) to ensure the asymptotic synchronization of the considered Lur'e system with a guaranteed $$H_{\infty }$$ performance. By solving the obtained LMIs, the required sampled-data control gain matrix is obtained, which assures the asymptotic stability of the error system and reduces the effect of external disturbance according to $$H_{\infty }$$ norm. Finally, the effectiveness and less conservatism of the proposed method are verified through numerical simulations of the Chua's circuit and neural networks. [ABSTRACT FROM AUTHOR]

This paper is concerned with the exponential H filtering problem for a class of discrete-time switched neural networks with random time-varying delays based on the sojourn-probability-dependent method. Using the average dwell time approach together with the piecewise Lyapunov function technique, sufficient conditions are proposed to guarantee the exponential stability for the switched neural networks with random time-varying delays which are characterized by introducing a Bernoulli stochastic variable. Based on the derived H performance analysis results, the H filter design is formulated in terms of Linear Matrix Inequalities (LMIs). Finally, two numerical examples are presented to demonstrate the effectiveness of the proposed design procedure. [ABSTRACT FROM AUTHOR]

In this paper, we study the hybrid projective synchronization problem for a class of fractional-order memristor-based neural networks with time delays. First, we address the basic ideas of fractional-order memristor-based neural networks (FMNNs) with hub structure and time delays. After that we derive the response system can be synchronized from the corresponding drive system, that is, the response system can be synchronized with the projection of the drive system generated through a design scaling matrix which is known as hybrid projective synchronization. By applying the Filippovs solutions, differential inclusion theory, stability theorem of linear fractional-order systems with multiple time delays and employing suitable linear feedback control law, some new sufficient conditions are derived to guaranteeing the projective synchronization of addressed FMNNs with hub structure and time delays. The analysis in this paper is based on the theory of fractional-order differential equations with discontinuous right-hand sides. Finally, a numerical example is presented to show the usefulness of our theoretical results. [ABSTRACT FROM AUTHOR]

In this paper, the model of memristor-based complex-valued neural networks (MCVNNs) with time-varying delays is established and the problem of passivity analysis for MCVNNs is considered and extensively investigated. The analysis in this paper employs results from the theory of differential equations with discontinuous right-hand side as introduced by Filippov. By employing the appropriate Lyapunov-Krasovskii functional, differential inclusion theory and linear matrix inequality (LMI) approach, some new sufficient conditions for the passivity of the given MCVNNs are obtained in terms of both complex-valued and real-value LMIs, which can be easily solved by using standard numerical algorithms. Numerical examples are provided to illustrate the effectiveness of our theoretical results. [ABSTRACT FROM AUTHOR]

This paper addresses the problem of stochastic sampled-data stabilization for neural-network-based control systems (NNBCSs) with an optimal guaranteed cost. In order to stabilize the closed-loop system, continuous-time nonlinear plant and three-layer fully connected feed-forward neural networks based on stochastic sampling are connected to the closed loop. By introducing new Lyapunov-Krasovskii functional with triple integral terms and by using second-order reciprocal convex technique, new stability and stabilization criteria for NNBCSs are derived in terms of linear matrix inequalities (LMIs). The desired stochastic sampled-data controllers can be calculated by solving these LMIs. Finally, physical example is given to verify the effectiveness and usefulness of the obtained results. [ABSTRACT FROM AUTHOR]

This study is concerned with the design of a non-fragile controller for an offshore steel jacket platform with nonlinear perturbations. The delay-dependent sufficient conditions are derived in terms of linear matrix inequalities based on suitable Lyapunov-Krasovskii functional, the second-order reciprocally convex approach and the lower bound lemma. The results indicate asymptotic stability of the offshore steel jacket platform utilizing the proposed non-fragile controller. Besides that, robust stability conditions are derived for an uncertain offshore platform subject to the non-fragile controller. A numerical example is given to illustrate the effectiveness of the proposed theoretical results. [ABSTRACT FROM AUTHOR]

In this paper, we extensively study the analysis of complete stability of complex-valued neural networks with time delay and impulsive effects. Using stability theory, impulsive effects and by constructing appropriate Lyapunov-Krasovskii functional, some sufficient conditions for the existence and complete stability of complex-valued neural networks with time delay and impulsive effects are derived in the form of complex-valued linear matrix inequality (LMIs) as well as real-valued LMIs. Finally, four numerical examples are given to establish the effectiveness of our theoretical results via standard numerical software. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the stability properties of a general class of nonlinear impulsive switched systems that include both stable and unstable subsystems. By using multiple Lyapunov-functions and the dwell-time approach, several criteria on globally exponential stability are established. It is shown that by suitably controlling the switching between the stable and unstable subsystems, the globally exponential stability of the nonlinear impulsive switched systems can be achieved. Finally, an example is given to show the effectiveness of the derived results. [ABSTRACT FROM AUTHOR]

In this paper, the problem of the existence, uniqueness and uniform stability of memristor-based fractional-order neural networks (MFNNs) with two different types of memductance functions is extensively investigated. Moreover, we formulate the complex-valued memristor-based fractional-order neural networks (CVMFNNs) with two different types of memductance functions and analyze the existence, uniqueness and uniform stability of such networks. By using Banach contraction principle and analysis technique, some sufficient conditions are obtained to ensure the existence, uniqueness and uniform stability of the considered MFNNs and CVMFNNs with two different types of memductance functions. The analysis results establish from the theory of fractional-order differential equations with discontinuous right-hand sides. Finally, four numerical examples are presented to show the effectiveness of our theoretical results. [ABSTRACT FROM AUTHOR]

In this paper, a fractional dynamical system of predator-prey with Holling type-II functional response and time delay is studied. Local and global stability of existence steady states and Hopf bifurcation with respect to the delay is investigated, with fractional-order $$0< \alpha \le 1$$ . It is found that Hopf bifurcation occurs when the delay passes through a sequence of critical values. Unconditionally, stable implicit scheme for the numerical simulations of the fractional-order delay differential model is introduced. The numerical simulations show the effectiveness of the numerical method and confirm the theoretical results. The presence of fractional order in the delayed differential model improves the stability of the solutions and enrich the dynamics of the model. [ABSTRACT FROM AUTHOR]

This paper investigates the problem of synchronization of identical and nonidentical memristor-based chaotic systems via active backstepping control technique. In order to achieve synchronization for identical chaotic systems, a memristor-based Lorenz system is considered as both master and slave systems, and for nonidentical chaotic systems, memristor-based Lorenz and Chuas systems are considered as master and slave systems, respectively. Based on the Lyapunov stability theory and active backstepping control technique, proper controllers are designed to achieve synchronization. Finally, numerical simulations are provided to show the effectiveness of the proposed controller. [ABSTRACT FROM AUTHOR]

In this paper, we study an issue of input-to-state stability analysis for a class of impulsive stochastic Cohen-Grossberg neural networks with mixed delays. The mixed delays consist of varying delays and continuously distributed delays. To the best of our knowledge, the input-to-state stability problem for this class of stochastic system has still not been solved, despite its practical importance. The main aim of this paper is to fill the gap. By constricting several novel Lyapunov-Krasovskii functionals and using some techniques such as the It $$\hat{o}$$ formula, Dynkin formula, impulse theory, stochastic analysis theory, and the mathematical induction, we obtain some new sufficient conditions to ensure that the considered system with/without impulse control is mean-square exponentially input-to-state stable. Moreover, the obtained results are illustrated well with two numerical examples and their simulations. [ABSTRACT FROM AUTHOR]

In this paper, we address the problem of exponential synchronization of Markovian jumping complex dynamical networks with mode-dependent time-varying coupling delay via a stochastic sampled-data controller. In addition, the sampling period is assumed to be time-varying and switches between $$m$$ different values in a random way with given probability. By constructing a new Lyapunov-Krasovskii functional (LKF) with triple integral terms and by employing convex combination technique and free weighting matrices method, sufficient conditions for the coupled complex dynamical network to be globally exponentially synchronized in the mean square sense are derived. The information about the lower bound of the discrete time-varying delay is used in the LKF. Based on the derived condition, the desired sampled-data feedback controller is designed in terms of the solution to linear matrix inequalities. Finally, two numerical examples are given to illustrate the effectiveness of the proposed methods. [ABSTRACT FROM AUTHOR]

This paper discusses the synchronization problem for a class of reaction-diffusion neural networks with Dirichlet boundary conditions. Unlike other studies, a sampled-data controller with stochastic sampling is designed in order to synchronize the concerned neural networks with reaction-diffusion terms and time-varying delays, where $$m$$ sampling periods are considered whose occurrence probabilities are given constants and satisfy the Bernoulli distribution. A novel discontinuous Lyapunov-Krasovskii functional with triple integral terms is introduced based on the extended Wirtinger's inequality. Using Jensen's inequality and reciprocally convex technique in deriving the upper bound for the derivative of the Lyapunov-Krasovskii functional, some new synchronization criteria are obtained in terms of linear matrix inequalities. Numerical examples are provided in order to show the effectiveness of the proposed theoretical results. [ABSTRACT FROM AUTHOR]

In this paper, the problem of finite-time stability of fractional-order complex-valued memristor-based neural networks (NNs) with time delays is extensively investigated. We first initiate the fractional-order complex-valued memristor-based NNs with the Caputo fractional derivatives. Using the theory of fractional-order differential equations with discontinuous right-hand sides, Laplace transforms, Mittag-Leffler functions and generalized Gronwall inequality, some new sufficient conditions are derived to guarantee the finite-time stability of the considered fractional-order complex-valued memristor-based NNs. In addition, some sufficient conditions are also obtained for the asymptotical stability of fractional-order complex-valued memristor-based NNs. Finally, a numerical example is presented to demonstrate the effectiveness of our theoretical results. [ABSTRACT FROM AUTHOR]

This paper first points out some fatal errors in the paper (Nonlinear Dyn 73:1367-1383, ). Then the main results of the above paper are corrected with some suitable modifications. The new feedback gain matrix is used to prove the estimation of the neuron states through numerical simulations with the same examples as discussed in the above paper. [ABSTRACT FROM AUTHOR]

This paper is concerned with the sampled-data state estimation problem for neural networks with both Markovian jumping parameters and leakage time-varying delays. Instead of the continuous measurement, the sampled measurement is used to estimate the neuron states, and a sampled-data estimator is constructed. In order to make full use of the sawtooth structure characteristic of the sampling input delay, a discontinuous Lyapunov functional is proposed based on the extended Wirtinger inequality. A less conservative delay dependent stability criterion is derived via constructing a new triple-integral Lyapunov-Krasovskii functional and the famous Jenson integral inequality. Based on the Lyapunov-Krasovskii functional approach, a state estimator of the considered neural networks has been achieved by solving some linear matrix inequalities, which can be easily facilitated by using the standard numerical software. Finally, two numerical examples are provided to show the effectiveness of the proposed methods. [ABSTRACT FROM AUTHOR]

In this paper, the sampled-data state estimation problem is investigated for neural networks with time-varying delays. Instead of the continuous measurement, the sampled measurement is used to estimate the neuron states, and a sampled data estimator is constructed. Based on the extended Wirtinger inequality, a discontinuous Lyapunov functional is introduced, which makes full use of the sawtooth structure characteristic of sampling input delay. New delay-dependent criteria are developed to estimate the neuron states through available output measurements such that the estimation error system is asymptotically stable. The criteria are formulated in terms of a set of linear matrix inequalities (LMIs), which can be checked efficiently by use of some standard numerical packages. Finally, a numerical example and its simulations are given to demonstrate the usefulness and effectiveness of the presented results. [ABSTRACT FROM AUTHOR]

This paper investigates the delay-probability-distribution-dependent stability problem of uncertain stochastic genetic regulatory networks (SGRNs) with time-varying delays. The information of the probability distribution of the time-delay is considered and transformed into parameter matrices of the transferred SGRNs model. Based on the Lyapunov-Krasovskii functional and a stochastic analysis approach, a delay-probability-distribution-dependent sufficient condition is obtained in the linear matrix inequality (LMI) form such that delayed SGRNs are robustly globally asymptotically stable in the mean square for all admissible uncertainties. Three numerical examples are given to illustrate the effectiveness of our theoretical results. [ABSTRACT FROM AUTHOR]

In this paper, a class of stationary oscillation of interval fuzzy cellular neural networks (FCNNs) with mixed delays under impulsive perturbations are considered. Mixed delays include discrete time-varying delays and unbounded distributed delays. By establishing a simple Lyapunov function, using impulsive differential inequality techniques and LMI techniques, some new sufficient criteria are obtained to ensure the existence, uniqueness and global exponential stability of stationary oscillation of interval FCNNs. The obtained results can be checked easily by the LMI control toolbox in MATLAB. Moreover, the results obtained in this paper are useful in the application and design of FCNNs, since the sufficient criteria are simple and easy to check in practice. A numerical example is given to illustrate the effectiveness of the obtained result. [ABSTRACT FROM AUTHOR]

This paper considers existence, uniqueness, and the global asymptotic stability for a class of High-order Hopfield neural networks with mixed delays and impulses. The mixed delays include constant delay in the leakage term (i.e., "leakage delay") and 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-dependent sufficient conditions are presented for the global asymptotic stability of the equilibrium point of the considered neural networks. These conditions are expressed in terms of LMI and can be easily checked by MATLAB LMI toolbox. In addition, two numerical examples are given to illustrate the applicability of the result. [ABSTRACT FROM AUTHOR]

This paper deals with the delay-dependent asymptotic stability analysis problem for a class of fuzzy bidirectional associative memory (BAM) neural networks with time delays in the leakage term by Takagi-Sugeno (T-S) fuzzy model. The nonlinear delayed BAM neural networks are first established as a modified T-S fuzzy model in which the consequent parts are composed of a set of BAM neural networks with time-varying delays. The parameter uncertainties are assumed to be norm bounded. Some new delay-dependent stability conditions are derived in terms of linear matrix inequality by constructing a new Lyapunov-Krasovskii functional and introducing some free-weighting matrices. Even there is no leakage delay, the obtained results are also less restrictive than some recent works. It can be applied to BAM neural networks with activation functions without assuming their boundedness, monotonicity, or differentiability. Numerical examples are given to demonstrate the effectiveness of the proposed methods. [ABSTRACT FROM AUTHOR]

Complex nonlinear systems can be represented to a set of linear sub-models by using fuzzy sets and fuzzy reasoning via ordinary Takagi-Sugeno (TS) fuzzy models. In this paper, the exponential stability of TS fuzzy bidirectional associative memory (BAM) neural networks with impulsive effect and time-varying delays is investigated. The model of fuzzy impulsive BAM neural networks with time-varying delays established as a modified TS fuzzy model is new in which the consequent parts are composed of a set of impulsive BAM neural networks with time-varying delays. Further the exponential stability for fuzzy impulsive BAM neural networks is presented by utilizing the Lyapunov-Krasovskii functional and the linear matrix inequality (LMI) technique without tuning any parameters. In addition, an example is provided to illustrate the applicability of the result using LMI control toolbox in MATLAB. [ABSTRACT FROM AUTHOR]

This paper deals with the problem of delay-dependent global robust asymptotic stability of uncertain switched Hopfield neural networks (USHNNs) with discrete interval and distributed time-varying delays and time delay in the leakage term. Some Lyapunov--Krasovskii functionals are constructed and the linear matrix inequality (LMI) approach are employed to derive some delay-dependent global robust stability criteria which guarantee the global robust asymptotic stability of the equilibrium point for all admissible parametric uncertainties. The proposed results that do not require the boundedness, differentiability, and monotonicity of the activation functions. Moreover, the stability behavior of USHNNs is very sensitive to the time delay in the leakage term. It can be easily checked via the LMI control toolbox in Matlab. In the absence of leakage delay, the results obtained are also new results. Finally, nine numerical examples are given to show the effectiveness of the proposed results. [ABSTRACT FROM AUTHOR]

Fuzzy cellular neural network (FCNN) structures are based on the uncertainties in human cognitive processes and in modeling neural systems, and they provide an interface between a human expert and classical cellular neural networks (CNNs). In this paper, an existence and global asymptotic stability analysis of the equilibrium point of FCNNs with time delay in the leakage term and unbounded distributed delays is investigated. Based on the Lyapunov-Krasovskii functional with free-weighting matrix, and using the homeomorphism mapping principle and linear matrix inequalities (LMIs), a new set of stability criteria for FCNNs is obtained with time delay in the leakage term, time-varying delays and unbounded distributed delays. The proposed results can be easily checked via the LMI Control Toolbox in MATLAB. Moreover, it is well known that the stability behavior of FCNNs is very sensitive to the time delay in the leakage term. In the absence of the leakage term, a new stability criterion is also derived by employing a Lyapunov-Krasovskii functional using an LMI approach. Numerical examples are provided to illustrate the effectiveness and reduced conservativeness of the developed techniques. [ABSTRACT FROM AUTHOR]

In this paper, the Takagi-Sugeno (T-S) fuzzy model representation is extended to the stability analysis for cellular neural networks (CNNs) with mixed time-varying delays and time delay in the leakage term via the delay decomposition approach. First, a sufficient condition is given to ensure the existence and uniqueness of equilibrium point by using topological degree theory. Then, we present global asymptotic stability of equilibrium point by using linear matrix inequality (LMI) approach and by constructing an augmented Lyapunov-Krasovskii functional (ALKF) together with convex combination method. The proposed results can be easily solved by some standard numerical packages. Finally, four numerical examples are given to demonstrate the effectiveness and conservativeness of our proposed results. [ABSTRACT FROM AUTHOR]

This paper is concerned with delay-dependent passivity analysis for delayed neural networks (DNNs) of neutral type. We first discuss the passivity conditions for DNNs without uncertainties and then extend this result to the case of interval uncertainties. By partitioning the delay intervals into multiple equidistant subintervals, some appropriate Lyapunov-Krasovskii functionals (LKFs) are constructed on these intervals. Considering these new LKFs and using free-weighting matrix approach, several new passivity criteria are proposed in terms of linear matrix inequalities, which are dependent on the size of the time delay. Finally, five numerical examples are given to illustrate the effectiveness and less conservatism of the developed techniques. [ABSTRACT FROM AUTHOR]