New delay-distribution-dependent stability analysis for discrete-time stochastic neural networks with randomly time-varying delays

An innovative stability analysis approach for a class of discrete-time stochastic neural networks (DSNNs) with time-varying delays is developed. By constructing a novel piecewise Lyapunov-Krasovskii functional candidate, a new sum inequality is presented to deal with sum items without ignoring any useful items, the model transformation is no longer needed, and the free weighting matrices are added to reduce the conservatism in the derivation of our results, so the improvement of computational efficiency can be expected. Numerical examples and simulations are also given to show the effectiveness and less conservatism of the proposed criteria.

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Delay-Probability-Distribution-Dependent Stability Analysis for Stochastic Neural Networks with Mixed Time-Varying Delays: The Discrete-Time Case

Advanced Materials Research ◽

10.4028/www.scientific.net/amr.217-218.600 ◽

2011 ◽

Vol 217-218 ◽

pp. 600-605

Author(s):

Xia Zhou ◽

Shou Ming Zhong

Keyword(s):

Neural Networks ◽

Stability Analysis ◽

Probability Distribution ◽

Discrete Time ◽

Time Delays ◽

Stochastic Neural Networks ◽

Time Varying ◽

Time Varying Delay ◽

Mixed Time Delays ◽

Varying Delay

The problem of delay-probability-distribution-dependent stability analysis for a class of discrete-time stochastic delayed neural networks (DSNNs) with mixed time delays is investigated. Here the mixed time delays are assumed to be discrete and distributed time delays and the uncertainties are assumed to be time varying norm bounded parameter uncertainties. The information of the probability distribution of the time-varying delay is considered and transformed into parameter matrices of the transferred DSNN model, in which the time-varying delay is characterized by introducing a Bernoulli stochastic variable. By constructing a new augmented Lyapunov-Krasovskii functional and introducing some new analysis techniques, a novel delay-probability-distribution-dependent stable criterion for the DSNN to be stable in the mean square sense are derived. These criteria are formulated in the forms of linear matrix inequalities.

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Robust stability analysis for discrete-time stochastic neural networks systems with time-varying delays

Applied Mathematics and Computation ◽

10.1016/j.amc.2008.12.084 ◽

2009 ◽

Vol 209 (2) ◽

pp. 305-313 ◽

Cited By ~ 50

Author(s):

Mengzhuo Luo ◽

Shouming Zhong ◽

Rongjun Wang ◽

Wei Kang

Keyword(s):

Neural Networks ◽

Stability Analysis ◽

Robust Stability ◽

Discrete Time ◽

Stochastic Neural Networks ◽

Time Varying ◽

Robust Stability Analysis

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Stability Analysis for Discrete-Time Stochastic Neural Networks with Mixed Time Delays via Delay-Paritioning

Advanced Materials Research ◽

10.4028/www.scientific.net/amr.228-229.464 ◽

2011 ◽

Vol 228-229 ◽

pp. 464-470

Author(s):

Xia Zhou ◽

Shou Ming Zhong

Keyword(s):

Neural Networks ◽

Stability Analysis ◽

Discrete Time ◽

Time Delays ◽

Optimization Problems ◽

Linear Matrix ◽

Stochastic Neural Networks ◽

Time Varying ◽

Parameter Uncertainties ◽

Mixed Time Delays

This paper revisits the problem of stability analysis for discrete-time stochastic neural networks (DSNNs) with mixed time-varying delays in the state. Here the mixed time delays are assumed to be discrete and distributed time delays and the uncertainties are assumed to be time varying norm bounded parameter uncertainties. A new delay-dependent stability criterion is presented by constructing a novel Lyapunov-Krasovskii functional and utilizing the delay partitioning idea and free-weighting matrix approach, Which is less conservative than the existing ones. This criterion can be developed in the frame of convex optimization problems and then solved via standard numerical software. These conditions are formulated in the forms of linear matrix inequalities, which feasibility can be easily checked by using Matlab LMI Toolbox.

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