Stability of impulsive hopfield neural networks with Markovian switching and time-varying delays

Ramachandran Raja; Rathinasamy Sakthivel; Selvaraj Marshal Anthoni; Hyunsoo Kim

International Journal of Applied Mathematics and Computer Science (2011)

  • Volume: 21, Issue: 1, page 127-135
  • ISSN: 1641-876X

Abstract

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The 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.

How to cite

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Ramachandran Raja, et al. "Stability of impulsive hopfield neural networks with Markovian switching and time-varying delays." International Journal of Applied Mathematics and Computer Science 21.1 (2011): 127-135. <http://eudml.org/doc/208028>.

@article{RamachandranRaja2011,
abstract = {The 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.},
author = {Ramachandran Raja, Rathinasamy Sakthivel, Selvaraj Marshal Anthoni, Hyunsoo Kim},
journal = {International Journal of Applied Mathematics and Computer Science},
keywords = {Hopfield neural networks; Markovian jumping; stochastic stability; Lyapunov function; impulses},
language = {eng},
number = {1},
pages = {127-135},
title = {Stability of impulsive hopfield neural networks with Markovian switching and time-varying delays},
url = {http://eudml.org/doc/208028},
volume = {21},
year = {2011},
}

TY - JOUR
AU - Ramachandran Raja
AU - Rathinasamy Sakthivel
AU - Selvaraj Marshal Anthoni
AU - Hyunsoo Kim
TI - Stability of impulsive hopfield neural networks with Markovian switching and time-varying delays
JO - International Journal of Applied Mathematics and Computer Science
PY - 2011
VL - 21
IS - 1
SP - 127
EP - 135
AB - The 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.
LA - eng
KW - Hopfield neural networks; Markovian jumping; stochastic stability; Lyapunov function; impulses
UR - http://eudml.org/doc/208028
ER -

References

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Citations in EuDML Documents

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  1. Qianhong Zhang, Lihui Yang, Daixi Liao, Existence and exponential stability of a periodic solution for fuzzy cellular neural networks with time-varying delays
  2. Yang Liu, Rongjiang Yang, Jianquan Lu, Bo Wu, Xiushan Cai, Stability analysis of high-order Hopfield-type neural networks based on a new impulsive differential inequality
  3. Qiaoling Chen, Zhidong Teng, Zengyun Hu, Bifurcation and control for a discrete-time prey-predator model with Holling-IV functional response
  4. Mai Viet Thuan, Vu Ngoc Phat, Hieu Trinh, Observer-based controller design of time-delay systems with an interval time-varying delay

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