Leakage Time-varying Delays Research Articles

Dissipativity and passivity analysis for memristor-based neural networks with leakage and two additive time-varying delays

Abstract In this paper, the problems of dissipativity and passivity analysis for memristor-based neural networks (MNNs) with both time-varying leakage delay and two additive time-varying delays are studied. By introducing an improved Lyapunov–Krasovskii functional (LKF) with triple integral terms, and combining the reciprocally convex combination technique, Wirtinger-based integral inequality with free-weighting matrices technique, some less conservative delay-dependent dissipativity and passivity criteria are obtained. The proposed criteria that depend on the upper bounds of the leakage and additive time-varying delays are given in terms of linear matrix inequalities (LMI), which can be solved by MATLAB LMI Control Toolbox. Meanwhile, the criteria for the system with a single time-varying delay are also provided. Finally, some examples are given to illustrate the effectiveness and superiority of the obtained results.

Almost automorphic solution for neutral type high-order Hopfield BAM neural networks with time-varying leakage delays on time scales

In this paper, by applying the exponential dichotomy theory on time scales, Banach contraction mapping principle and differential inequality analysis techniques, we establish some sufficient conditions for the existence and global exponential stability of almost automorphic solution for neutral type high-order Hopfield bidirectional associative memory (BAM) neural networks with time-varying leakage delays on time scales. In the addressed system, we not only consider the effects of the first-order neutral terms on networks, but also investigate the influences of the second-order neutral terms on the networks. High-order Hopfield BAM neural networks with continuously distributed leakage delays on time scales are also considered. Our results are completely new even if time scale T=R or T=Z and complementary to the previously existing results. Finally, three examples with numerical simulations are presented to illustrate the feasibility of our proposed theoretical results.

The Sampled-data Exponential Stability of BAM with Distributed Leakage Delays

This paper investigates the exponential stability of bidirectional associative memory (BAM) neural networks with distributed leakage delays and sampled-data state feedback input. Based on the input delay approach, the considered BAM neural networks is transformed into a system with mixed distributed leakage delays and time-varying discrete delays. Some sufficient conditions are given to ensure that the system is exponentially stable. Finally, a numerical example is provided to demonstrate the effectiveness of the theoretical analysis.

Delay-partitioning approach to stability analysis of state estimation for neutral-type neural networks with both time-varying delays and leakage term via sampled-data control

ABSTRACTThis paper mainly focuses on further improved stability analysis of state estimation for neutral-type neural networks with both time-varying delays and leakage delay via sampled-data control by delay-partitioning approach. Instead of the continuous measurement, the sampled measurement is used to estimate the neuron states and a sampled-data estimator is constructed. To fully use the sawtooth structure characteristics of the sampling input delay, sufficient conditions are derived such that the system governing the error dynamics is asymptotically stable. The design method of the desired state estimator is proposed. We construct a suitable Lyapunov–Krasovskii functional (LKF) with triple and quadruple integral terms then by using a novel free-matrix-based integral inequality (FMII) including well-known integral inequalities as special cases. Moreover, the design procedure can be easily achieved by solving a set of linear matrix inequalities (LMIs), which can be easily facilitated by using the standard numerical software. Finally, two numerical examples are given to demonstrate the effectiveness of the proposed results.

Adaptive Exponential Synchronization for Stochastic Competitive Neural Networks with Time-Varying Leakage Delays and Reaction-Diffusion Terms

We study the exponential synchronization problem for a class of stochastic competitive neural networks with different timescales, as well as spatial diffusion, time-varying leakage delays, and discrete and distributed time-varying delays. By introducing several important inequalities and using Lyapunov functional technique, an adaptive feedback controller is designed to realize the exponential synchronization for the proposed competitive neural networks in terms of p-norm. According to the theoretical results obtained in this paper, the influences of the timescale, external stimulus constants, disposable scaling constants, and controller parameters on synchronization are analyzed. Numerical simulations are presented to show the feasibility of the theoretical results.

New Results of Global Asymptotical Stability for Impulsive Hopfield Neural Networks with Leakage Time-Varying Delay

In this paper, Hopfield neural networks with impulse and leakage time-varying delay are considered. New sufficient conditions for global asymptotical stability of the equilibrium point are derived by using Lyapunov-Kravsovskii functional, model transformation and some analysis techniques. The criterion of stability depends on the impulse and the bounds of the leakage time-varying delay and its derivative, and is presented in terms of a linear matrix inequality (LMI).

Pseudo Almost Periodic Solutions for High-Order Hopfield Neural Networks with Time-Varying Leakage Delays

In this paper, high-order Hopfield neural networks with time-varying leakage delays are investigated. By applying Lyapunov functional method and differential inequality techniques, a set of sufficient conditions are obtained for the existence and exponential stability of pseudo almost periodic solutions of the model. Some simulations are carried out to support the theoretical findings. Our results improve and generalize those of the previous studies.

H∞ State Estimation for Stochastic Markovian Jumping Neural Network with Time-Varying Delay and Leakage Delay

The H∞ state estimation problem for a class of stochastic neural networks with Markovian jumping parameters and leakage delay is investigated in this paper. By employing a suitable Lyapunov functional and inequality technic, the sufficient conditions for exponential stability as well as prescribed H∞ norm level of the state estimation error system are proposed and verified, and all obtained results are expressed in terms of strict linear matrix inequalities (LMIs). Examples and simulations are presented to show the effectiveness of the proposed methods, at the same time, the effect of leakage delay on stability of neural networks system and on the attenuation level of state estimator are discussed.

Dissipativity and passivity analysis for discrete-time T–S fuzzy stochastic neural networks with leakage time-varying delays based on Abel lemma approach

In this paper, the problem of dissipativity and passivity analysis for discrete-time T–S fuzzy stochastic neural networks with leakage time-varying delays is investigated based on Abel lemma approach. In order to obtain less conservative results, Jensen inequality, free-weighting matrix approach and Wirtinger-based inequality have been intensively used in the context of time delay systems. In parallel, the above-mentioned approaches have also been applied to discrete time-delay systems. However, it is well-known that these inequalities may introduce an undesirable conservatism in the dissipativity and passivity conditions in the existing available literature. In this paper, we propose an alternative inequality based on Abel lemma, more precisely on the Abel lemma-based finite sum inequalities. By constructing suitable Lyapunov–Krasovskii functional and using the stochastic analysis technique, strictly (Q,S,R)−γ-dissipativity and passivity conditions are derived to the concerned neural networks. The proposed criterion that depends on the upper bounds of the leakage time-varying delay is given in terms of linear matrix inequalities, which can be solved by MATLAB LMI Control Toolbox. Finally, numerical examples are shown to demonstrate the usefulness and effectiveness of the proposed methods.

Effects of bounded and unbounded leakage time-varying delays in memristor-based recurrent neural networks with different memductance functions

This paper is concerned with the problem of μ-stability analysis of memristor-based recurrent neural networks with the effects of bounded and unbounded leakage time-varying delays. A new idea of μ-stability analysis of neural networks is given first, then by means of the linear matrix inequality (LMI) approach, stability criteria are presented. Two types of memductance functions is used to derive the proposed stability results. Obviously, the memristive neural network with different memductance functions is a state-dependent switched system or a state-dependent continuous system, which is the generalization of those for conventional artificial neural networks. Under the framework of Filippov solutions, μ-stability analysis of solutions for functional differential inclusions and memristor-based neural networks can be guaranteed by constructing suitable Lyapunov–Krasovskii functionals, suitable inequalities and LMIs. The dynamic analysis in this paper utilizes the theory of set-valued maps and functional differential equations with discontinuous right-hand sides of Filippov type. Leakage time-varying delay is considered in this paper to be bounded, unbounded and differentiable. Taking into account of the information of the neuron activation functions and unbounded time-varying delays, several improved results have been obtained in terms of LMIs and these are tested by MATLAB LMI toolbox. The model based on the memristor widens the relevance scope for the design of neural networks, and the new effective results also enrich the toolbox for the qualitative analysis of neural networks. Finally, numerical examples are provided to demonstrate the effectiveness of the proposed theoretical results.

New synchronization criteria for an array of neural networks with hybrid coupling and time-varying delays

This paper is concerned with the global exponential synchronization for an array of hybrid coupled neural networks with time-varying leakage delay, discrete and distributed delays. Applying a novel Lyapunov functional and the property of outer coupling matrices of the neural networks, sufficient conditions are obtained for the global exponential synchronization of the system. The derived synchronization criteria are closely related with the time-varying delays and the coupling structure of the networks. The maximal allowable upper bounds of the time-varying delays can be obtained guaranteeing the global synchronization for the neural networks. The method we adopt in this paper is different from the commonly used linear matrix inequality (LMI) technique, and our synchronization conditions are new, which are easy to check in comparison with the previously reported LMI-based ones. Some examples are given to show the effectiveness of the obtained theoretical results.

Robust stability analysis for discrete-time neural networks with time-varying leakage delays and random parameter uncertainties

This paper is concerned with the problem of robust stability analysis for discrete-time neural networks with time-varying coupling delays, random parameter uncertainties and time-varying leakage delays. The uncertainties enter into the system parameters in a random way and such randomly occurring uncertainties obey certain mutually uncorrelated Bernoulli-distributed white noise sequences. The important feature of the results reported here is that the probability of occurrence of the parameter uncertainties are known a priori. Constructing suitable Lyapunov–Krasovskii functional (LKF) terms, sufficient conditions ensuring the stability of the discrete-time neural networks are derived in terms of linear matrix inequalities (LMIs). Finally, numerical examples are rendered to exemplify the effectiveness of the proposed results.

Dissipativity and Passivity Analysis of Markovian Jump Neural Networks with Two Additive Time-Varying Delays

In this paper, we investigated a problem of dissipativity and passivity analysis of Markovian jump neural networks involving two additive time-varying delays. By considering proper triple integral terms in the Lyapunov---Krasovskii functional, several sufficient conditions are derived for verifying the dissipativity criteria of neural networks. The relationship between the time-varying delay and its lower and upper bounds is taken into account when estimating the upper bound of the time delay. As a result, some improved delay dissipativity criteria for neural networks with two additive time-varying delays components are proposed. The dissipativity criteria that depend on the upper bounds of the leakage time-varying delay and its derivative is given in terms of linear matrix inequalities, which can be efficiently solved via standard numerical software. Finally, three numerical examples are given to show the effectiveness of the proposed results.

Pseudo Almost Periodic Solutions for HCNNs with Time-Varying Leakage Delays

Abstract In this paper, we consider a class of high-order cellular neural networks (HCNNs) model with time-varying delays in the leakage terms. We give some sufficient conditions which guarantee the exponential stability of pseudo almost periodic solutions for the model. The obtained results complement with some recent ones in the literature.The technique of proof involves the exponential dichotomy theory and the fixed point theorem. An illustrative example is given with an application.

Exponential Stability for Stochastic Neural Networks with Time-Varying Delay and Leakage Delay

This paper investigates the exponential stability problem for a class of stochastic neural networks with leakage delay. By employing a suitable Lyapunov functional and stochastic stability theory technic, the sufficient conditions which make the stochastic neural networks system exponential mean square stable are proposed and proved. All results are expressed in terms of linear matrix inequalities (LMIs). Example and simulation are presented to show the effectiveness of the proposed method.

Stability of Stochastic Discrete-Time Neural Networks with Discrete Delays and the Leakage Delay

This paper investigates the stability of stochastic discrete-time neural networks (NNs) with discrete time-varying delays and leakage delay. As the partition of time-varying and leakage delay is brought in the discrete-time system, we construct a novel Lyapunov-Krasovskii function based on stability theory. Furthermore sufficient conditions are derived to guarantee the global asymptotic stability of the equilibrium point. Numerical example is given to demonstrate the effectiveness of the proposed method and the applicability of the proposed method.

Existence and stability of pseudo almost periodic solutions for shunting inhibitory cellular neural networks with neutral type delays and time-varying leakage delays

In this paper, shunting inhibitory cellular neural networks(SICNNs) with neutral type delays and time-varying leakage delays are investigated. By applying Lyapunov functional method and differential inequality techniques, a set of sufficient conditions are obtained for the existence and exponential stability of pseudo almost periodic solutions of the model. An example is given to support the theoretical findings. Our results improve and generalize those of the previous studies.

Robust stability analysis for discrete-time uncertain neural networks with leakage time-varying delay

This paper is concerned with the stability problem for a class of discrete-time neural networks with time-varying delays in network coupling, parameter uncertainties and time-delay in the leakage term. By constructing triple Lyapunov–Krasovskii functional terms, based on Lyapunov method, new sufficient conditions are established to ensure the asymptotic stability of discrete-time delayed neural networks system. Convex reciprocal technique is incorporated to deal with double summation terms and the stability criteria are presented in terms of linear matrix inequalities (LMIs). Finally numerical examples are exploited to substantiate the theoretical results. It has also shown that the derived conditions are less conservative than the existing results in the literature.

New result on convergence for HCNNs with time-varying leakage delays

This paper is devoted to further studying on the exponential convergence for a class of high-order cellular neural networks with time-varying leakage delays. Based on the inequality techniques, some sufficient conditions are derived to ensure that all solutions of the addressed system converge exponentially to zero vector. Moreover, an example and its numerical simulation are given to illustrate the main result.

New exponential convergence on SICNNs with time-varying leakage delays and neutral type distributed delays

This paper is concerned with a shunting inhibitory cellular neural networks (SICNNs) with time-varying leakage delays and neutral type continuously distributed delays. Some criteria are established for the existence and global exponential stability of pseudo almost periodic solutions for the addressed model with pseudo almost periodic coefficients and delays. Moreover, without assuming pseudo almost periodicity on coefficients and delays, a novel criterion is also given to ensure that all solutions of the considered neural networks converge exponentially to zero vector, which is new and complement previously known results.