Stochastic stability analysis of fuzzy hopfield neural networks with time-varying delays

The ordinary Takagi-Sugeno (TS) fuzzy models have provided an approach to represent complex nonlinear systems to a set of linear sub-models by using fuzzy sets and fuzzy reasoning. In this paper, stochastic fuzzy Hopfield neural networks with time-varying delays (SFVDHNNs) are studied. The model of SFVDHNN is first established as a modified TS fuzzy model in which the consequent parts are composed of a set of stochastic Hopfield neural networks with time-varying delays. Secondly, the global exponential stability in the mean square for SFVDHNN is studied by using the Lyapunov-Krasovskii approach. Stability criterion is derived in terms of linear matrix inequalities (LMIs), which can be effectively solved by some standard numerical packages.     

Global asymptotic stability and global exponential stability of neural networks with unbounded time-varying delays

This brief studies the global asymptotic stability and the global exponential stability of neural networks with unbounded time-varying delays and with bounded and Lipschitz continuous activation functions. Several sufficient conditions for the global exponential stability and global asymptotic stability of such neural networks are derived. The new results given in the brief extend the existing relevant stability results in the literature to cover more general neural networks.     

Global asymptotic stability of cellular neural networks with unequal delays: LMI approach

A criterion for the global asymptotic stability and uniqueness of the equilibrium point of cellular neural networks with unequal delays is presented. The criterion is computationally efficient, since it is in the form of linear matrix inequality (LMI).     

LMI approach for global periodicity of neural networks with time-varying delays

This paper investigates the global periodicity of neural networks with time-varying delays. Several conditions guaranteeing the existence, uniqueness, and global asymptotical and exponential stability of periodic solution are obtained. These criteria are expressed in terms of linear matrix inequalities, thus they can be efficiently verified. Moreover, according to the criteria, the maximal bound of time delays and the fastest convergence speed can also be estimated for the exponential periodicity of neural networks. Some examples are given to illustrate the effectiveness of the given criteria.     

Delay-dependent exponential stability of delayed neural networks with time-varying delay

In this brief, free-weighting matrices are employed to express the relationship between the terms in the Leibniz-Newton formula; and based on that relationship, a new delay-dependent exponential-stability criterion is derived for delayed neural networks with a time-varying delay. Two numerical examples demonstrate the improvement this method provides over existing ones.     

Global stability in hopfield neural networks with distributed time delays

In this paper, without assuming the boundedness, monotonicity and differentiability of the activation functions, the conditions ensuring existence, uniqueness, and global asymptotical stability of the equilibrium point of Hopfield neural network models with distributed time delays are studied. Using M-matrix theory and constructing proper Liapunov functionals, the sufficient conditions for global asymptotic stability are obtained.     

Global stability of a class of neural networks with time-varying delay

This paper presents a new sufficient condition for the uniqueness and global asymptotic stability of the equilibrium point for a class of neural networks with time-varying delays. The result is obtained by the use of a more general type of Lyapunov-Krasovskii functional, establishing a relation between the network parameters of the neural system and time-varying delay parameter. The result is also shown to be a generalization of a previously published result.     

Global robust stability analysis of neural networks with multiple time delays

Global robust convergence properties of continuous-time neural networks with discrete delays are studied. By employing suitable Lyapunov functionals, we derive a set of delay-independent sufficient conditions for the existence, uniqueness, and global robust asymptotic stability of the equilibrium point. The conditions can be easily verified as they can be expressed in terms of the network parameters only. Some numerical examples are given to compare our results with previous robust stability results derived in the literature. One of our main results is shown to improve and generalize a previously published result. Other results proved to establish a new set of robust stability criteria for delayed neural networks.     

Local stability of REM algorithm with time-varying delays

We investigate the local stability in equilibrium for an Internet congestion control algorithm proposed by Low (see IEEE/ACM Transactions on Networking, vol.7, p.861-875,1999). The network consists of multisource and one-bottleneck link with heterogenous time-varying propagation delays. Linear matrix inequality (LMI) stability criteria is presented for discrete congestion control algorithm of TCP/REM dual model, which can be efficiently and easily solved by the LMI toolbox provided by Matlab software. An important feature is to acquire the maximum network delays to guarantee the stability of congestion control algorithm, i.e., the scale stability domain of REM algorithm.     

ON THE STABILITY OF CELLULAR NEURAL NETWORKS WITH FEEDBACK MODE

Cellular Neural Networks (CNN) with feedback mode and M×N cells are equivalent to a network which possesses 2M×N cells, a neighborhood with mirror-like structure, space-variant templates and without feedback as well as without input templates. The stability of the CNN with feedback mode and transformations with the neighborhood of mirror-like structure are discussed.     

Global asymptotic stability of a class of neural networks with distributed delays

In this paper, the problem of stability analysis for a class of neural networks with distributed delays is investigated. Applying the M-matrix theory and new analysis technique, novel sufficient conditions for the existence, uniqueness, and global asymptotic stability of the equilibrium point of neural networks with distributed delays are derived. The new stability criteria can be applied to the case when the nondelayed terms cannot dominate the delayed terms, which have great significance in the design and application of neural networks with distributed delays. Three illustrative examples are presented which demonstrate the usefulness of the proposed results.     

Global exponential stability and periodicity of recurrent neural networks with time delays

In this paper, the global exponential stability and periodicity of a class of recurrent neural networks with time delays are addressed by using Lyapunov functional method and inequality techniques. The delayed neural network includes the well-known Hopfield neural networks, cellular neural networks, and bidirectional associative memory networks as its special cases. New criteria are found to ascertain the global exponential stability and periodicity of the recurrent neural networks with time delays, and are also shown to be different from and improve upon existing ones.     

Global asymptotic and robust stability of recurrent neural networks with time delays

In this paper, two related problems, global asymptotic stability (GAS) and global robust stability (GRS) of neural networks with time delays, are studied. First, GAS of delayed neural networks is discussed based on Lyapunov method and linear matrix inequality. New criteria are given to ascertain the GAS of delayed neural networks. In the designs and applications of neural networks, it is necessary to consider the deviation effects of bounded perturbations of network parameters. In this case, a delayed neural network must be formulated as a interval neural network model. Several sufficient conditions are derived for the existence, uniqueness, and GRS of equilibria for interval neural networks with time delays by use of a new Lyapunov function and matrix inequality. These results are less restrictive than those given in the earlier references.     

Conditions of asymptotic stability for cellular neural networks with time delay

In this paper, global asymptotic stability for cellular neural networks with time delay is discussed using a novel Liapunov function. Some novel sufficient conditions for global asymptotic stability are obtained. Those results are simple and practical than those given by P. P. Civalleri, et al., and have a leading importance to design cellular neural networks with time delay.     

Invariance principle and complete stability for cellular neural networks

In applications of classification of patterns, image processing, associative memories etc, the complete stability of cellular neural networks (CNNs) plays an important role. Invariance principles based on the Lyapunov functions and functionals are still the most advantageous theory to analyze the complete stability. However, one difficulty in applying classical invariance principles to the complete stability is to prove that the largest invariant set consists of equilibrium points. In this paper, we present one invariance principle to analyze the complete stability. We can avoid the difficulty of proving that the largest invariant set is constituted of equilibrium points in discussing some sufficient condition for complete stability of CNNs by using this invariance principle.     

Global asymptotic stability and global exponential stability of delayed cellular neural networks

In this brief, many novel theorems and corollaries are presented regarding the global asymptotic stability and global exponential stability of cellular neural networks with constant and variable time delays. The stability conditions in the new results improve and generalize existing ones. Several examples are discussed to compare the new results with the existing ones.     

A comment on "Globally exponential stability of neural networks with variable delays"

For original paper by Jiye Zhang see IEE Transactions on Circuits & Systems I, vol. 50, No.2, p.288-90, Feb. 2003.     

Robust power control of CDMA cellular radio systems with time-varying delays

Power control is an important factor to increase communication link quality and system capacity in the direct-sequence code-division multiple access (DS-CDMA) cellular radio systems. The Smith prediction filter can achieve the unbiased asymptotic tracking about a desired target signal to interference noise ratio (SINR) under the fixed round-trip delay. However, it is sensitive to the variation of round-trip delay. In order to track the desired SINR with the time-varying round-trip delay, a multiple-mode Smith prediction filter, which combines the multiple Smith predictors with a likelihood function, is proposed for the power control of CDMA systems. The proposed scheme can compensate for the unknown time-varying round-trip delay. Simulation results show that the performance of the proposed multiple-mode power control method is robust to time-varying round-trip delay in the CDMA cellular radio systems.     

New results for exponential stability of delayed cellular neural networks

This brief presents new sufficient conditions for the global exponential stability of the equilibrium point for delayed cellular neural networks (DCNNs). It is shown that the use of a more general type of Lyapunov-Krasovskii functional enables us to derive new results for exponential stability of the equilibrium point for DCNNs. The results establish a relation between the delay time and the parameters of the network. The results are also compared with one of the most recent results derived in the literature.     

Synchronization of coupled connected neural networks with delays

We investigate synchronization of an array of linearly coupled identical connected neural networks with delays; Variational method is used to investigate local synchronization. Global exponential stability is studied, too. We do not assume that the coupling matrix A is symmetric or irreducible. The linear matrix inequality approach is used to judge synchronization with global convergence property.