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Robust stochastic convergence and stability of neutral‐type neural networks with Markovian jump and mixed delays
Author(s) -
Zheng ChengDe,
Lv Xixi,
Liang Wenlong,
Wang Zhanshan
Publication year - 2015
Publication title -
international journal of adaptive control and signal processing
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.73
H-Index - 66
eISSN - 1099-1115
pISSN - 0890-6327
DOI - 10.1002/acs.2461
Subject(s) - mathematics , exponential stability , control theory (sociology) , convex combination , convergence (economics) , artificial neural network , regular polygon , computer science , convex optimization , nonlinear system , physics , control (management) , quantum mechanics , artificial intelligence , machine learning , economics , economic growth , geometry
Summary The robust stochastic convergence and stability in mean square are investigated for a class of uncertain neutral‐type neural networks with both Markovian jump parameters and mixed delays. First, by employing the Lyapunov method and a generalized Halanay‐type inequality for stochastic differential equations, a delay‐dependent condition is derived to guarantee the state variables of the discussed neural networks to be globally uniformly exponentially stochastic convergent to a ball in the state space with a prespecified convergence rate. Next, by applying the Jensen integral inequality and a novel reciprocal convex lemma, a delay‐dependent criterion is developed to achieve the globally robust stochastic stability in mean square. With some parameters being fixed in advance, the proposed conditions are all expressed in terms of LMIs, which can be solved numerically by employing the standard MATLAB LMI toolbox package. Finally, two illustrated examples are given to show the effectiveness and less conservatism of the obtained results over some existing works. Copyright © 2014 John Wiley & Sons, Ltd.