Decomposition approach to the stability of recurrent neural networks with asynchronous time delays in quaternion field
In this paper, the global exponential stability for recurrent neural networks (QVNNs) with asynchronous time delays is investigated in quaternion field. Due to the non-commutativity of quaternion multiplication resulting from Hamilton rules: ij=−ji=k, jk=−kj=i, ki=−ik=j, ijk=i2=j2=k2=−1, the QVNN is...
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| Veröffentlicht in: | Neural networks 2017-10, Vol.94, p.55-66 |
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| creator | Zhang, Dandan Kou, Kit Ian Liu, Yang Cao, Jinde |
| description | In this paper, the global exponential stability for recurrent neural networks (QVNNs) with asynchronous time delays is investigated in quaternion field. Due to the non-commutativity of quaternion multiplication resulting from Hamilton rules: ij=−ji=k, jk=−kj=i, ki=−ik=j, ijk=i2=j2=k2=−1, the QVNN is decomposed into four real-valued systems, which are studied separately. The exponential convergence is proved directly accompanied with the existence and uniqueness of the equilibrium point to the consider systems. Combining with the generalized ∞-norm and Cauchy convergence property in the quaternion field, some sufficient conditions to guarantee the stability are established without using any Lyapunov–Krasovskii functional and linear matrix inequality. Finally, a numerical example is given to demonstrate the effectiveness of the results. |
| doi_str_mv | 10.1016/j.neunet.2017.06.014 |
| format | Article |
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Due to the non-commutativity of quaternion multiplication resulting from Hamilton rules: ij=−ji=k, jk=−kj=i, ki=−ik=j, ijk=i2=j2=k2=−1, the QVNN is decomposed into four real-valued systems, which are studied separately. The exponential convergence is proved directly accompanied with the existence and uniqueness of the equilibrium point to the consider systems. Combining with the generalized ∞-norm and Cauchy convergence property in the quaternion field, some sufficient conditions to guarantee the stability are established without using any Lyapunov–Krasovskii functional and linear matrix inequality. Finally, a numerical example is given to demonstrate the effectiveness of the results.</description><identifier>ISSN: 0893-6080</identifier><identifier>EISSN: 1879-2782</identifier><identifier>DOI: 10.1016/j.neunet.2017.06.014</identifier><identifier>PMID: 28753445</identifier><language>eng</language><publisher>United States: Elsevier Ltd</publisher><subject>Asynchronous time delay ; Global exponential stability ; Linear matrix inequality ; Neural Networks (Computer) ; Quaternion-valued neural network ; Time Factors</subject><ispartof>Neural networks, 2017-10, Vol.94, p.55-66</ispartof><rights>2017 Elsevier Ltd</rights><rights>Copyright © 2017 Elsevier Ltd. 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Finally, a numerical example is given to demonstrate the effectiveness of the results.</description><subject>Asynchronous time delay</subject><subject>Global exponential stability</subject><subject>Linear matrix inequality</subject><subject>Neural Networks (Computer)</subject><subject>Quaternion-valued neural network</subject><subject>Time Factors</subject><issn>0893-6080</issn><issn>1879-2782</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2017</creationdate><recordtype>article</recordtype><sourceid>EIF</sourceid><recordid>eNp9kE1v1DAQhi0EokvhHyDkI5cEf8VxLkio5UuqxAXO1iSeaL0k9tZ2Wu2_x6stHDnN5X3nmXkIectZyxnXHw5twC1gaQXjfct0y7h6Rnbc9EMjeiOekx0zg2w0M-yKvMr5wBjTRsmX5EqYvpNKdTvycItTXI8x--JjoHA8pgjTnpZIyx5pLjD6xZcTjTNNOG0pYSi0khMsdZTHmH5n-ujLnkI-hWmfYohbpsWvSB0ucMrUB3q_QcEUzojZ4-JekxczLBnfPM1r8uvL558335q7H1-_33y6ayapRWlUB44zJWehesnGoUMjEUYwpodulk4acL1mMCA6oXtgDsDhILRTAx8FyGvy_rK3vnW_YS529XnCZYGA9UzLB6F0BWhdo-oSnVLMOeFsj8mvkE6WM3s2bg_2YtyejVumbTVea--eCNu4ovtX-qu4Bj5eAlj_fPCYbJ48hgmdr0KLddH_n_AHcn-XoQ</recordid><startdate>201710</startdate><enddate>201710</enddate><creator>Zhang, Dandan</creator><creator>Kou, Kit Ian</creator><creator>Liu, Yang</creator><creator>Cao, Jinde</creator><general>Elsevier Ltd</general><scope>CGR</scope><scope>CUY</scope><scope>CVF</scope><scope>ECM</scope><scope>EIF</scope><scope>NPM</scope><scope>AAYXX</scope><scope>CITATION</scope><scope>7X8</scope></search><sort><creationdate>201710</creationdate><title>Decomposition approach to the stability of recurrent neural networks with asynchronous time delays in quaternion field</title><author>Zhang, Dandan ; Kou, Kit Ian ; Liu, Yang ; Cao, Jinde</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c362t-45ad1043f24730b95e83eaba887a5f3d38ad760a9eed267a0daade926d491b2a3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2017</creationdate><topic>Asynchronous time delay</topic><topic>Global exponential stability</topic><topic>Linear matrix inequality</topic><topic>Neural Networks (Computer)</topic><topic>Quaternion-valued neural network</topic><topic>Time Factors</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Zhang, Dandan</creatorcontrib><creatorcontrib>Kou, Kit Ian</creatorcontrib><creatorcontrib>Liu, Yang</creatorcontrib><creatorcontrib>Cao, Jinde</creatorcontrib><collection>Medline</collection><collection>MEDLINE</collection><collection>MEDLINE (Ovid)</collection><collection>MEDLINE</collection><collection>MEDLINE</collection><collection>PubMed</collection><collection>CrossRef</collection><collection>MEDLINE - Academic</collection><jtitle>Neural networks</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Zhang, Dandan</au><au>Kou, Kit Ian</au><au>Liu, Yang</au><au>Cao, Jinde</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Decomposition approach to the stability of recurrent neural networks with asynchronous time delays in quaternion field</atitle><jtitle>Neural networks</jtitle><addtitle>Neural Netw</addtitle><date>2017-10</date><risdate>2017</risdate><volume>94</volume><spage>55</spage><epage>66</epage><pages>55-66</pages><issn>0893-6080</issn><eissn>1879-2782</eissn><abstract>In this paper, the global exponential stability for recurrent neural networks (QVNNs) with asynchronous time delays is investigated in quaternion field. 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| subjects | Asynchronous time delay Global exponential stability Linear matrix inequality Neural Networks (Computer) Quaternion-valued neural network Time Factors |
| title | Decomposition approach to the stability of recurrent neural networks with asynchronous time delays in quaternion field |
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