Global asymptotic stability of uncertain stochastic bi-directional associative memory networks with discrete and distributed delays
In this paper, the global asymptotic stability analysis problem is investigated for a class of stochastic bi-directional associative memory (BAM) networks with mixed time-delays and parameter uncertainties. The mixed time-delays consist of both the discrete and the distributed delays, the uncertaint...
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| Published in | Mathematics and computers in simulation Vol. 80; no. 3; pp. 490 - 505 |
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| Main Authors | , , |
| Format | Journal Article |
| Language | English |
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Elsevier B.V
01.11.2009
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| ISSN | 0378-4754 1872-7166 |
| DOI | 10.1016/j.matcom.2008.07.007 |
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| Abstract | In this paper, the global asymptotic stability analysis problem is investigated for a class of stochastic bi-directional associative memory (BAM) networks with mixed time-delays and parameter uncertainties. The mixed time-delays consist of both the discrete and the distributed delays, the uncertainties are assumed to be norm-bounded, and the neural network are subject to stochastic disturbances described by a Brownian motion. Without assuming the monotonicity and differentiability of activation functions, we employ the Lyapunov–Krasovskii stability theory and some new developed techniques to establish sufficient conditions for the stochastic delayed BAM networks to be globally asymptotically stable in the mean square. These conditions are expressed in terms of the feasibility to a set of linear matrix inequalities (LMIs) that can be easily checked by utilizing the numerically efficient Matlab LMI toolbox. A simple example is exploited to show the usefulness of the derived LMI-based stability conditions. |
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| AbstractList | In this paper, the global asymptotic stability analysis problem is investigated for a class of stochastic bi-directional associative memory (BAM) networks with mixed time-delays and parameter uncertainties. The mixed time-delays consist of both the discrete and the distributed delays, the uncertainties are assumed to be norm-bounded, and the neural network are subject to stochastic disturbances described by a Brownian motion. Without assuming the monotonicity and differentiability of activation functions, we employ the Lyapunov–Krasovskii stability theory and some new developed techniques to establish sufficient conditions for the stochastic delayed BAM networks to be globally asymptotically stable in the mean square. These conditions are expressed in terms of the feasibility to a set of linear matrix inequalities (LMIs) that can be easily checked by utilizing the numerically efficient Matlab LMI toolbox. A simple example is exploited to show the usefulness of the derived LMI-based stability conditions. |
| Author | Shu, Huisheng Lü, Zengwei Wang, Zidong |
| Author_xml | – sequence: 1 givenname: Huisheng surname: Shu fullname: Shu, Huisheng organization: School of Information Sciences and Technology, Donghua University, Shanghai 200051, China – sequence: 2 givenname: Zidong surname: Wang fullname: Wang, Zidong email: Zidong.Wang@brunel.ac.uk organization: School of Information Sciences and Technology, Donghua University, Shanghai 200051, China – sequence: 3 givenname: Zengwei surname: Lü fullname: Lü, Zengwei organization: Department of Applied Mathematics, Donghua University, Shanghai 200051, China |
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| CitedBy_id | crossref_primary_10_1109_TNNLS_2011_2182659 crossref_primary_10_1007_s11571_012_9200_6 crossref_primary_10_1016_j_neucom_2013_01_039 crossref_primary_10_1155_2013_180717 crossref_primary_10_1155_2011_569141 crossref_primary_10_1155_2013_629621 crossref_primary_10_1007_s11571_010_9135_8 crossref_primary_10_1186_s13662_018_1553_7 crossref_primary_10_1155_2012_890512 crossref_primary_10_1016_j_neucom_2013_12_044 crossref_primary_10_1080_00207160_2010_500374 crossref_primary_10_1016_j_neucom_2010_09_011 crossref_primary_10_1016_j_matcom_2010_08_011 crossref_primary_10_1016_j_neucom_2018_05_062 |
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| Keywords | Global asymptotic stability Linear matrix inequality Lyapunov–Krasovskii functionals Discrete and distributed delays Bi-directional associative memory neural networks |
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| SubjectTerms | Bi-directional associative memory neural networks Discrete and distributed delays Global asymptotic stability Linear matrix inequality Lyapunov–Krasovskii functionals |
| Title | Global asymptotic stability of uncertain stochastic bi-directional associative memory networks with discrete and distributed delays |
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