Commenced in January 2007
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Edition: International
Paper Count: 4

globally exponential stability Related Publications

4 Globally Exponential Stability and Dissipativity Analysis of Static Neural Networks with Time Delay

Authors: Shouming Zhong, Yucai Ding, Lijiang Xiang

Abstract:

The problems of globally exponential stability and dissipativity analysis for static neural networks (NNs) with time delay is investigated in this paper. Some delay-dependent stability criteria are established for static NNs with time delay using the delay partitioning technique. In terms of this criteria, the delay-dependent sufficient condition is given to guarantee the dissipativity of static NNs with time delay. All the given results in this paper are not only dependent upon the time delay but also upon the number of delay partitions. Two numerical examples are used to show the effectiveness of the proposed methods.

Keywords: Time Delay, globally exponential stability, Dissipativity, Static neural networks

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3 Exponential State Estimation for Neural Networks with Leakage, Discrete and Distributed Delays

Authors: Shouming Zhong, Liyuan Wang

Abstract:

In this paper, the design problem of state estimator for neural networks with the mixed time-varying delays are investigated by constructing appropriate Lyapunov-Krasovskii functionals and using some effective mathematical techniques. In order to derive several conditions to guarantee the estimation error systems to be globally exponential stable, we transform the considered systems into the neural-type time-delay systems. Then with a set of linear inequalities(LMIs), we can obtain the stable criteria. Finally, three numerical examples are given to show the effectiveness and less conservatism of the proposed criterion.

Keywords: Neural Networks, globally exponential stability, State estimator

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2 ψ-exponential Stability for Non-linear Impulsive Differential Equations

Authors: Bhanu Gupta, Sanjay K. Srivastava

Abstract:

In this paper, we shall present sufficient conditions for the ψ-exponential stability of a class of nonlinear impulsive differential equations. We use the Lyapunov method with functions that are not necessarily differentiable. In the last section, we give some examples to support our theoretical results.

Keywords: lyapunov function, exponential stability, impulsive differential equations, globally exponential stability, ψ-stability

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1 Existence and Globally Exponential Stability of Equilibrium for BAM Neural Networks with Mixed Delays and Impulses

Authors: Shouming Zhong, Xiaomei Wang

Abstract:

In this paper, a class of generalized bi-directional associative memory (BAM) neural networks with mixed delays is investigated. On the basis of Lyapunov stability theory and contraction mapping theorem, some new sufficient conditions are established for the existence and uniqueness and globally exponential stability of equilibrium, which generalize and improve the previously known results. One example is given to show the feasibility and effectiveness of our results.

Keywords: Equilibrium, existence, mixed delays, globally exponential stability, Bi-directional associative memory (BAM) neural networks, Lyapunov stability theory, contraction mapping theorem

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