Effect of leakage delay on the almost periodic solutions of fuzzy cellular neural networks

ABSTRACT

In this paper, fuzzy cellular neural networks with time-varying delays in leakage terms are investigated. With the help of the differential inequality theory and almost periodic function theory, a set of sufficient criteria that guarantee the existence and exponential stability of almost periodic solutions of fuzzy cellular neural networks with time-varying delays in leakage terms are established. Our results are new and complement some previously known ones. Moreover, numerical simulations are carried out to verify our theoretical results.     

时变滞后随机大系统的稳定性：向量Lyapunov函数法

本文研究变系数、变时滞线性随机大系统的均方渐近稳定性，通过将Ｈａｌａｎａｙ不等式推广到高维空间、采用向量Ｌｙａｐｕｎｏｖ函数、运用Ｍ－矩阵等工具，得到了随机大系统的稳定性判据，文中模型考虑了子系统之间的交互随机干扰，所得稳定性判断是滞后无关的。     

Stability results for Takagi–Sugeno fuzzy uncertain BAM neural networks with time delays in the leakage term

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.

     

Global robust asymptotic stability analysis of uncertain switched Hopfield neural networks with time delay in the leakage term

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.     

Effect of Proportional Delays and Continuously Distributed Leakage Delays on Global Exponential Convergence of CNNS

This paper is concerned with a class of cellular neural networks (CNNs) with proportional delays and continuously distributed leakage delays. Using the differential inequality theory, a set of sufficient conditions which guarantee the exponential convergence of all solutions of CNNs with proportional delays and continuously distributed leakage delays are derived. Computer simulations are carried out to verify our theoretical findings. The obtained results of this paper are new and complement some previous studies.     

The stabilization of BAM neural networks with time-varying delays in the leakage terms via sampled-data control

This paper is concerned with the stabilization of bidirectional associative memory neural networks with time-varying delays in the leakage terms using sampled-data control. We apply an input delay approach to change the sampling system into a continuous time-delay system. Based on the Lyapunov theory, some stability criteria are obtained. These conditions are expressed in terms of linear matrix inequalities and can be solved via standard numerical software. Finally, one numerical example is given to demonstrate the effectiveness of the proposed results.     

Exponential convergence for HRNNs with continuously distributed delays in the leakage terms

This paper considers exponential convergence for a class of high-order recurrent neural networks (HRNNs) with continuously distributed delays in the leakage terms (i.e., “leakage delays”). Without assuming the boundedness on the activation functions, some sufficient conditions are derived to ensure that all solutions of this system converge exponentially to zero point by using Lyapunov functional method and differential inequality techniques, which are new and complement previously known results. In particular, we propose a new approach to prove the exponential convergence of HRNNs with continuously distributed delays in the leakage terms. Moreover, an example is given to show the effectiveness of the proposed method and results.     

具有多时变时滞的单一和复合线性系统的时滞无关稳定性判据

针对单一和复合多时变时滞系统分别建立了稳定性的充分条件,结果的推导采用了拉什密辛（Ｒａｚｕ－ｍｉｋｈｉｎ）定理结合代数不等式的方法,同时,本文提出了一些优化稳定性判据中参数的方法,所建判据既不依赖于时滞的大小也不依赖时滞的导数,故既适用于时变时滞系统也适用于常时滞系统或无无时滞系统,最后,给出了一些例子所提方法的应用,并比较文献中存在的结果。     

Novel results on stability analysis of neutral-type neural networks with additive time-varying delay components and leakage delay

The objective of this paper is to analyze the stability analysis of neutral-type neural networks with additive time-varying delay and leakage delay. By constructing a suitable augmented Lyapunov-Krasovskii functional with triple and four integral terms, some new stability criteria are established in terms of linear matrix inequalities, which is easily solved by various convex optimization techniques. More information of the lower and upper delay bounds of time-varying delays are used to derive the stability criteria, which can lead less conservative results. The obtained conditions are expressed with linear matrix inequalities (LMIs) whose feasible can be checked easily by MATLAB LMI control toolbox. Finally, two numerical examples are given to demonstrate the effectiveness of the proposed method.

     

Convergence for HRNNs with Unbounded Activation Functions and Time-varying Delays in the Leakage Terms

In this paper, the exponential convergence problems are considered for a class of high-order recurrent neural networks (HRNNs) with time-varying delays in the leakage terms. Without assuming the boundedness on the activation functions, some sufficient conditions are derived to ensure that all solutions of this system converge exponentially to zero point by using Lyapunov functional method and differential inequality techniques. It is believed that these results are significant and useful for the design and applications of HRNNs. Even for the system without leakage delays, the criterion is shown to be different from a recent publication. Moreover, some examples are given to show the effectiveness of the proposed method and results.     

New results on almost periodic solutions for CNNs with time-varying leakage delays

In this paper, based on the exponential dichotomy theory and contraction mapping fixed point theorem, we obtain some sufficient conditions ensuring the global exponential stability of almost periodic solutions for a new generalized cellular neural network model with time-varying delays in leakage (or forgetting) terms. Our results complement some recent ones. Moreover, an illustrative example and its numerical simulation are given to demonstrate the effectiveness of the obtained results.     

Asymptotic stability criteria for a two-neuron network with different time delays

In this paper, the asymptotic stability of a two-neuron system with different time delays has been investigated. Some criteria for determining the global asymptotically stability of equilibrium are derived from the theory of monotonic dynamical system and the approach of Lyapunov functional. For local asymptotic stability, some elegant criteria are also obtained by the Nyquist criteria. We find that one of them depends on the length of delays while the other ones do not. In the latter case, the delays are sometimes called harmless delays. The results obtained have leading significance in the study of neural networks composed of a large number of neurons with different time delays.     

Delay-range-dependent robust stabilization for uncertain T-S fuzzy control systems with interval time-varying delays

This paper is concerned with robust stabilization for a class of T-S fuzzy control systems with interval time-varying delays. An approach is proposed to significantly improve the system performance while reducing the number of scalar decision variables in linear matrix inequalities. The main points of the approach are: (i) two coupling integral inequalities are proposed to deal with some integral items in the derivation of the stability criteria; (ii) an appropriate Lyapunov-Krasovskii functional is constructed by including both the lower and upper bounds of the interval time-varying delays; and (iii) neither model transformation nor free weighting matrices are employed in the theoretical result derivation. As a result, some improved sufficient stability criteria are derived, and the maximum allowable delay bound and controller gains can be obtained simultaneously by solving an optimization problem. Numerical examples are given to demonstrate the effectiveness of the proposed approach.     

Global exponential convergence of neutral-type competitive neural networks with multi-proportional delays,distributed delays and time-varying delay in leakage delays

This paper is concerned with a class of neutral-type competitive neural networks with multi-proportional delays, distributed delays and leakage delays. By employing the differential inequality theory, some sufficient conditions are given to ensure that all solutions of the addressed system converge exponentially to zero vector. An illustrative example is also given at the end of this paper to show the effectiveness of our results.     

Finite-time boundedness of state estimation for semi-Markovian jump systems with distributed leakage delay and linear fractional uncertainties

In this paper, the problem of finite-time bounded control for uncertain semi-Markovian jump neural networks with mixed delays which include distributed leakage delay (DLD) and mixed time-varying delays is considered. The system not only contains semi-Markovian jump, linear fractional uncertainties (LFUs), mixed time-varying delays but also includes distributed time delays in the leakage term which is not yet investigated in existing papers. Firstly, uncertainty parameters in the systems are solved by LFU based on the new model. Secondly, a novel augmented Lyapunov–Krasovskii functional (LKF) which involves more information about time-varying delays is constructed. Moreover, latest integral inequalities and time-delays division method are used to estimate the derivative of proposed LKFs. Thirdly, in the framework of uncertainty, semi-Markovian jump, DLD, mixed delays and external disturbance, a full-order state estimator is constructed such that the error dynamic system is finite-time bounded under the condition of given linear matrix inequalities. Finally, usefulness and advantages of the obtained results are verified by three numerical examples.     

Further results on delay-distribution-dependent robust stability criteria for delayed systems

This paper concerns the robust stability analysis of uncertain systems with time delays as random variables drawn from some probability distribution. The delay-distribution-dependent criteria for the exponential stability of the original system in mean square sense are achieved by Lyapunov functional method and the linear matrix inequality (LMI) technique. The proposed approach involves neither free weighting matrices nor any model transformation, and it shows that the new criteria can provide less conservative results than some existing ones. Numerical examples are given to demonstrate the effectiveness and the benefits of the proposed method.     

Stochastic stability for uncertain genetic regulatory networks with interval time-varying delays

This paper is concerned with the robust asymptotic stability analysis for uncertain genetic regulatory networks with both interval time-varying delays and stochastic noise. By using the stochastic analysis approach, employing some free-weighting matrices and introducing an appropriate type of Lyapunov functional which takes into account the ranges of delays, some new delay-range-dependent and rate-dependent stability criteria are established in terms of linear matrix inequalities (LMIs) to guarantee the delayed genetic regulatory networks to be robustly asymptotically stable in the mean square. As a result, the new criteria are applicable to both fast and slow time-varying delays. Five numerical examples are also used to demonstrate the usefulness of the main results and less conservativeness of the proposed method.