Stability Of Cellular Neural Networks Research Articles

A Novel Delay-Dependent Criterion for Global Power Stability of Cellular Neural Networks with Proportional Delay

The global power stability of a class of cellular neural networks with proportional delay is considered in this paper. By proposing a new integral inequality and constructing a Lyapunov functional candidate, a novel delay-dependent condition formulated by linear matrix inequalities is derived to ensure that the equilibrium point of the addressed networks achieves global power stability. The proposed criteria complement and improve some existing results in the recent publications, and their effectiveness and advantage are demonstrated by two numerical examples.

Analysis of associative memories based on cellular neural networks with value-varying templates

ABSTRACTIn many research literatures, the dynamical behaviour of cellular neural networks (CNNs) is simplified by using cloning template. However, the flaws of cloning template are obvious, because the correlation between weights of cells in CNNs is enhanced. In order to overcome the shortcomings of cloning template, value-varying templates can be used in CNNs. In this paper, associative memories based on CNNs with value-varying templates are investigated. A criterion about stability of CNNs is presented. Then, the problem about obtaining parameters of CNNs can be translated into a problem of solving linear equations for each cell. A design procedure of associative memories is given by our theories and methods. From the procedure, the parameters of CNNs can be obtained. Finally, three examples are used to demonstrate the effectiveness of our theories and methods. And the results show that success rate of associative memories is higher than previous methods.

Further Improvement on Delay-Dependent Global Robust Exponential Stability for Delayed Cellular Neural Networks with Time-Varying Delays

This paper is concerned with global robust exponential stability for a class of delayed cellular neural networks with time-varying delays. Some new sufficient conditions are presented for the uniqueness of equilibrium point and the global stability of cellular neural networks with time varying delay by constructing Lyapunov functional and using linear matrix inequality and the integral inequality approach. Numerical examples are illustrated to show the effectiveness of the proposed method. From the simulation results, significant improvement over the recent results can be observed.

周期多比例时滞细胞神经网络全局渐近稳定性的平均准则

本文致力于研究带有周期系数和多比例时滞细胞神经网络的全局渐近稳定性。首先，通过研究微分不等式的渐近稳定性，我们给出一类周期泛函微分方程的渐近稳定性准则；其次，利用获得的稳定性结果和非线性测度方法，我们给出该类神经网络的全局渐近稳定性准则，我们的研究结果是现有相关结果的部分推广；最后，一个例子被提供以说明我们结果的正确性。 This paper is devoted to studying global asymptotic stability of cellular neural networks with periodic coefficients and multi-proportional delays. Firstly, through studying the asymptotic stability of the differential inequality, we give the asymptotic stability criterion of a class of periodic functional differential equations. Secondly, we obtain an integral average criterion for global asymptotic stability of the cellular neural networks by means of the result we obtain and the nonlinear measure method, and our study result is partial generalization of some existing results. Finally, we use an example to illustrate the correctness of our result.

Global exponential stability of cellular neural networks with multi-proportional delays

In this paper, a class of cellular neural networks (CNNs) with multi-proportional delays is studied. The nonlinear transformation yi(t) = xi( e t) transforms a class of CNNs with multi-proportional delays into a class of CNNs with multi-constant delays and time-varying coefficients. By applying Brouwer fixed point theorem and constructing the delay differential inequality, several delay-independent and delay-dependent sufficient conditions are derived for ensuring the existence, uniqueness and global exponential stability of equilibrium of the system and the exponentially convergent rate is estimated. And several examples and their simulations are given to illustrate the effectiveness of obtained results.

Global asymptotic stability of CNNs with impulses and multi‐proportional delays

This paper is devoted to global asymptotic stability of cellular neural networks with impulses and multi‐proportional delays. First, by means of the transformation vi(t) = ui(et), the impulsive cellular neural networks with proportional delays are transformed into impulsive cellular neural networks with the variable coefficients and constant delays. Second, we prove the global exponential stability of the latter by nonlinear measure, and that the exponential stability of the latter implies the asymptotic stability of the former. We furthermore provide a sufficient condition to the existence, uniqueness, and the global asymptotic stability of the equilibrium point of the former. Our results are generalizations of some existing ones. Finally, an example and its simulation are presented to illustrate effectiveness of our method. Copyright © 2015 John Wiley & Sons, Ltd.

Delay-Dependent Stability of Cellular Neural Networks with Multiple Delays

Back propagation (BP) neural network is used to approximate the dynamic character of nonlinear discrete-time system. Considering the unmodeling dynamics of the system, the weights of neural network are updated by using a dead-zone algorithm and a robust adaptive controller based on the BP neural network is proposed. For the situation that jumping change parameters exist, multiple neural networks with multiple weights are built to cover the uncertainty of parameters, and multiple controllers based on these models are set up. At every sample time, a performance index function based on the identification error will be used to choose the optimal model and the corresponding controller. Different kinds of combinations of fixed model and adaptive model will be used for robust multiple models adaptive control (MMAC). The proof of stability and convergence of MMAC are given, and the significant efficacy of the proposed methods is tested by simulation. This paper deals with the problem of delay-dependent stability criterion of delay-difference system with multiple delays of cellular neural networks. Based on quadratic Lyapunov functional approach and free-weighting matrix approach, some linear matrix inequality criteria are found to guarantee delay-dependent asymptotical stability of these systems. And one example illustrates the exactness of the proposed criteria.

Global asymptotic stability of cellular neural networks with proportional delays

Proportional delay, which is different from distributed delay, is a kind of unbounded delay. The proportional delay system as an important mathematical model often rises in some fields such as physics, biology systems, and control theory. In this paper, the uniqueness and the global asymptotic stability of equilibrium point of cellular neural networks with proportional delays are analyzed. By using matrix theory and constructing suitable Lyapunov functional, delay-dependent and delay-independent sufficient conditions are obtained for the global asymptotic stability of cellular neural networks with proportional delays. These results extend previous works on these issues for the delayed cellular neural networks. Two numerical examples and their simulation are given to illustrate the effectiveness of obtained results.

Asymptotic stability of cellular neural networks with multiple proportional delays

Proportional delay is a kind of unbounded time-varying delay, which is different from unbounded distributed delays. In this paper, asymptotic stability of the equilibrium point of cellular neural networks with multiple proportional delays is presented. Sufficient conditions for delay-dependent global asymptotic stability and delay-independent uniform asymptotic stability of the system are obtained by employing matrix theory and constructing Lyapunov functional. Two examples are given to illustrate the effectiveness of the obtained results and less conservative than previously existing results.

An LMI Approach for Dynamics of Switched Cellular Neural Networks with Mixed Delays

This paper considers the dynamics of switched cellular neural networks (CNNs) with mixed delays. With the help of the Lyapnnov function combined with the average dwell time method and linear matrix inequalities (LMIs) technique, some novel sufficient conditions on the issue of the uniformly ultimate boundedness, the existence of an attractor, and the globally exponential stability for CNN are given. The provided conditions are expressed in terms of LMI, which can be easily checked by the effective LMI toolbox in Matlab in practice.

Delay-Dependent Exponential Stability of Cellular Neural Networks with Multi-Proportional Delays

Global exponential stability of a class of cellular neural networks with multi-proportional delays is investigated. New delay-dependent sufficient conditions ensuring global exponential stability for the system presented here are related to the size of the proportional delay factor, by employing matrix theory and Lyapunov functional, and without assuming the differentiability, boundedness and monotonicity of the activation functions. Two examples and their simulation results are given to illustrate the effectiveness of the obtained results.

Complete stability of cellular neural networks with unbounded time-varying delays

In this paper, we are concerned with the delayed cellular neural networks (DCNNs) in the case that the time-varying delays are unbounded. Under some conditions, it shows that the DCNNs can exhibit 3(n) equilibrium points. Then, we track the dynamics of u(t)(t>0) in two cases with respect to different types of subset regions in which u(0) is located. It concludes that every solution trajectory u(t) would converge to one of the equilibrium points despite the time-varying delays, that is, the delayed cellular neural networks are completely stable. The method is novel and the results obtained extend the existing ones. In addition, two illustrative examples are presented to verify the effectiveness of our results.

Analysis and design of associative memories based on stability of cellular neural networks

It is well known that the prototype patterns in associative memories can be represented by stable equilibrium points of cellular neural networks (CNNs). Therefore, the stability of equilibrium points of CNNs is critical in associative memories based on CNNs. In this paper, some criteria about the stability of CNNs are established. In fact, these criteria give some constraint conditions for the relationship of parameters of CNNs. Compared with the previous works, our results relax the conservatism of the relationship of parameters and extend the range of the values of parameters. Two design procedures on the parameters of CNNs are given to achieve associative memories under our criteria. Finally, an example is given to verify the theoretical results and design procedures.

Impulsive control on global exponential stability for cellular neural networks with supremums

In this paper, the problem of global exponential stability for impulsive cellular neural networks with time-varying delays and supremums over a past interval of time is studied. The impulses are realized at fixed moments of time and can be considered as a control. We establish several stability criteria by employing Lyapunov functions and the Razumikhin technique. These results can easily be used to design and verify globally stable networks.

Analysis of associative memories based on stability of cellular neural networks with time delay

In the paper, associative memories based on cellular neural networks with time delay are presented. In some previous papers, the relationship between cloning templates is closer and stronger. Therefore, some methods are used to make the relationship loose. First, some theories on stability of cellular neural networks are given. Then, associative memories based on cellular neural networks are given on the basis of these theories. In addition, a design procedure of associative memories is introduced. Finally, some examples are given to verify the theoretical results and design procedures.

Fixed Point and Asymptotic Analysis of Cellular Neural Networks

We firstly employ the fixed point theory to study the stability of cellular neural networks without delays and with time‐varying delays. Some novel and concise sufficient conditions are given to ensure the existence and uniqueness of solution and the asymptotic stability of trivial equilibrium at the same time. Moreover, these conditions are easily checked and do not require the differentiability of delays.

Delay-Dependent Robust Stability of Cellular Neural Networks with Time-Varying Discrete and Distributed Delay

Delay-dependent robust stability of neural networks with discrete and distributed delays is considered in this paper. Stability criteria are derived in LMIs avoiding bounding certain cross terms and the restriction of derivative of time-varying delay is removed. Numerical examples are given to indicate significant improvements over some existing results.

Global exponential stability of mixed discrete and distributively delayed cellular neural network

This paper concernes analysis for the global exponential stability of a class of recurrent neural networks with mixed discrete and distributed delays. It first proves the existence and uniqueness of the balance point, then by employing the Lyapunov—Krasovskii functional and Young inequality, it gives the sufficient condition of global exponential stability of cellular neural network with mixed discrete and distributed delays, in addition, the example is provided to illustrate the applicability of the result.

On global exponential stability for impulsive cellular neural networks with time-varying delays

In this paper, the problem of global exponential stability for cellular neural networks (CNNs) with time-varying delays and fixed moments of impulsive effect is studied. A new sufficient condition has been presented ensuring the global exponential stability of the equilibrium points by using piecewise continuous Lyapunov functions and the Razumikhin technique combined with Young’s inequality. The results established here extend those given previously in the literature. Compared with the method of Lyapunov functionals as in most previous studies, our method is simpler and more effective for stability analysis.

Stability of cellular neural networks with time varying delay

In this paper, the global asymptotic stability of a class of delayed cellular neural networks is studied. Some new sufficient conditions are presented for the uniqueness of equilibrium point and the global stability of cellular neural networks with time varying delay by constructing Lyapunov functional and using linear matrix inequality (LMI). A numerical example is presented to illustrate the effectiveness of our theoretical results.