GLOBAL EXPONENTIAL STABILITY OF FUZZY INTERVAL DELAYED NEURAL NETWORKS WITH IMPULSES ON TIME SCALES

In this paper, we investigate the existence and uniqueness of equilibrium point for fuzzy interval delayed neural networks with impulses on time scales. And we give the criteria of the global exponential stability of the unique equilibrium point for the neural networks under consideration using Lyapunov method. Finally, we present an example to illustrate that our results are effective.

RELAXED STABILITY CONDITIONS FOR DELAYED RECURRENT NEURAL NETWORKS WITH POLYTOPIC UNCERTAINTIES

This paper investigates the problem of stability analysis for recurrent neural networks with time-varying delays and polytopic uncertainties. Parameter-dependent Lypaunov functionals are employed to obtain sufficient conditions that guarantee the robust global exponential stability of the equilibrium point of the considered neural network. The derived stability criteria are expressed in terms of a set of relaxed linear matrix inequalities, which can be easily tested by using commercially available software. Two numerical examples are provided to demonstrate the effectiveness of the proposed results.

DELAY-DEPENDENT ROBUST EXPONENTIAL STABILITY FOR UNCERTAIN RECURRENT NEURAL NETWORKS WITH TIME-VARYING DELAYS

This paper considers the problem of robust exponential stability for a class of recurrent neural networks with time-varying delays and parameter uncertainties. The time delays are not necessarily differentiable and the uncertainties are assumed to be time-varying but norm-bounded. Sufficient conditions, which guarantee that the concerned uncertain delayed neural network is robustly, globally, exponentially stable for all admissible parameter uncertainties, are obtained under a weak assumption on the neuron activation functions. These conditions are dependent on the size of the time delay and expressed in terms of linear matrix inequalities. Numerical examples are provided to demonstrate the effectiveness and less conservatism of the proposed stability results.

New stability criteria for uncertain neural networks with interval time-varying delays

This paper is concerned with the stability analysis for neural networks with interval time-varying delays and parameter uncertainties. An approach combining the Lyapunov-Krasovskii functional with the differential inequality and linear matrix inequality techniques is taken to investigate this problem. By constructing a new Lyapunov-Krasovskii functional and introducing some free weighting matrices, some less conservative delay-derivative-dependent and delay-derivative-independent stability criteria are established in term of linear matrix inequality. And the new criteria are applicable to both fast and slow time-varying delays. Three numerical examples show that the proposed criterion are effective and is an improvement over some existing results in the literature.

A new approach to exponential stability analysis of neural networks with time-varying delays

This paper considers the problem of exponential stability analysis of neural networks with time-varying delays. The activation functions are assumed to be globally Lipschitz continuous. A linear matrix inequality (LMI) approach is developed to derive sufficient conditions ensuring the delayed neural network to have a unique equilibrium point, which is globally exponentially stable. The proposed LMI conditions can be checked easily by recently developed algorithms solving LMIs. Examples are provided to demonstrate the reduced conservativeness of the proposed results.

Stability analysis of a delayed Hopfield neural network

In this paper, we study a class of neural networks, which includes bidirectional associative memory networks and cellular neural networks as its special cases. By Brouwer's fixed point theorem, a continuation theorem based on Gains and Mawhin's coincidence degree, matrix theory, and inequality analysis, we not only obtain some different sufficient conditions ensuring the existence, uniqueness, and global exponential stability of the equilibrium but also estimate the exponentially convergent rate. Our results are less restrictive than previously known criteria and can be applied to neural networks with a broad range of activation functions assuming neither differentiability nor strict monotonicity.

Effect of transmission delay on the rate of convergence of a class of nonlinear contractive dynamical systems

We investigate the qualitative properties of a general class of contractive dynamical systems with time delay by using a unified analysis approach for any p-contraction with p in [1,infinity]. It is proved that the delayed contractive dynamical system is always globally exponentially stable no matter how large the time delay is, while the rate of convergence of the delayed system is reduced as the time delay increases. A lower bound on the rate of convergence of the delayed contractive dynamical system is obtained, which is the unique positive solution of a nonlinear equation with three parameters, namely, the time delay, the time constant and the p-contraction constant in the system. We show that the previously established results in the literature about the global asymptotic or exponential stability independent of delay for Hopfield-type neural networks can actually be deduced by recasting the network model into the general framework of contractive dynamical systems with some p-contraction (p in [1,infinity]) under the given delay-independent stability conditions. Numerical simulation examples are also presented to illustrate the obtained theoretical results.