Delay-dependent stochastic stability criteria for Markovian jumping neural networks with mode-dependent time-varying delays and partially known transition rates

2012 ◽  
Vol 218 (9) ◽  
pp. 5769-5781 ◽  
Author(s):  
Junkang Tian ◽  
Yongming Li ◽  
Jinzhou Zhao ◽  
Shouming Zhong
Keyword(s):  
Neural Networks ◽  
Stochastic Stability ◽  
Time Varying ◽  
Transition Rates ◽  
Stability Criteria ◽  
Markovian Jumping ◽  
Partially Known Transition Rates ◽  
Delay Dependent

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.

scholarly journals Stability of impulsive Hopfield neural networks with Markovian switching and time-varying delays

2011 ◽  
Vol 21 (1) ◽  
pp. 127-135 ◽  
Author(s):  
Ramachandran Raja ◽  
Rathinasamy Sakthivel ◽  
Selvaraj Anthoni ◽  
Hyunsoo Kim
Keyword(s):  
Neural Networks ◽  
Hopfield Neural Networks ◽  
Markovian Switching ◽  
Linear Matrix ◽  
Time Varying ◽  
Matrix Inequalities ◽  
Stability Criteria ◽  
Markovian Jumping ◽  
Discrete State ◽  
Delay Dependent

Stability of impulsive Hopfield neural networks with Markovian switching and time-varying delaysThe paper is concerned with stability analysis for a class of impulsive Hopfield neural networks with Markovian jumping parameters and time-varying delays. The jumping parameters considered here are generated from a continuous-time discrete-state homogenous Markov process. By employing a Lyapunov functional approach, new delay-dependent stochastic stability criteria are obtained in terms of linear matrix inequalities (LMIs). The proposed criteria can be easily checked by using some standard numerical packages such as the Matlab LMI Toolbox. A numerical example is provided to show that the proposed results significantly improve the allowable upper bounds of delays over some results existing in the literature.

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