New stochastic stability criteria of Hopfield neural networks with Markovian jump parameters

2008 ◽  
Author(s):  
Gui-Ju Shi ◽  
Ji-Qing Qiu ◽  
Jing-Chen ◽  
Hai-Kuo He ◽  
Guo-Gang Li
Keyword(s):  
Neural Networks ◽  
Stochastic Stability ◽  
Hopfield Neural Networks ◽  
Stability Criteria ◽  
Markovian Jump ◽  
Markovian Jump Parameters

scholarly journals Stochastic Stability of Neural Networks with Both Markovian Jump Parameters and Continuously Distributed Delays

2009 ◽  
Vol 2009 ◽  
pp. 1-20 ◽  
Author(s):  
Quanxin Zhu ◽  
Jinde Cao
Keyword(s):  
Neural Networks ◽  
Stochastic Stability ◽  
Distributed Delays ◽  
Linear Matrix ◽  
Matrix Inequalities ◽  
Computationally Efficient ◽  
Markovian Jump ◽  
Markovian Jump Parameters ◽  
Finite State ◽  
Theoretical Results

The problem of stochastic stability is investigated for a class of neural networks with both Markovian jump parameters and continuously distributed delays. The jumping parameters are modeled as a continuous-time, finite-state Markov chain. By constructing appropriate Lyapunov-Krasovskii functionals, some novel stability conditions are obtained in terms of linear matrix inequalities (LMIs). The proposed LMI-based criteria are computationally efficient as they can be easily checked by using recently developed algorithms in solving LMIs. A numerical example is provided to show the effectiveness of the theoretical results and demonstrate the LMI criteria existed in the earlier literature fail. The results obtained in this paper improve and generalize those given in the previous literature.

Robust Stochastic Stability of Discrete-Time Markovian Jump Neural Networks with Leakage Delay

2014 ◽  
Vol 69 (1-2) ◽  
pp. 70-80 ◽  
Author(s):  
Mathiyalagan Kalidass ◽  
Hongye Su ◽  
Sakthivel Rathinasamy
Keyword(s):  
Neural Networks ◽  
Discrete Time ◽  
Stochastic Stability ◽  
Leakage Delay ◽  
Linear Matrix ◽  
Stability Criteria ◽  
Markovian Jumping ◽  
Weighting Matrix ◽  
The Stability ◽  
Delay Dependent

This paper presents a robust analysis approach to stochastic stability of the uncertain Markovian jumping discrete-time neural networks (MJDNNs) with time delay in the leakage term. By choosing an appropriate Lyapunov functional and using free weighting matrix technique, a set of delay dependent stability criteria are derived. The stability results are delay dependent, which depend on not only the upper bounds of time delays but also their lower bounds. The obtained stability criteria are established in terms of linear matrix inequalities (LMIs) which can be effectively solved by some standard numerical packages. Finally, some illustrative numerical examples with simulation results are provided to demonstrate applicability of the obtained results. It is shown that even if there is no leakage delay, the obtained results are less restrictive than in some recent works.

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