{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2022,11,16]],"date-time":"2022-11-16T05:20:39Z","timestamp":1668576039256},"reference-count":51,"publisher":"Emerald","issue":"4","license":[{"start":{"date-parts":[[2022,4,14]],"date-time":"2022-04-14T00:00:00Z","timestamp":1649894400000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.emerald.com\/insight\/site-policies"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["GS"],"published-print":{"date-parts":[[2022,11,16]]},"abstract":"Purpose<\/jats:title>The purpose of this paper is to study the dynamic behavior of complex-valued switched grey neural network models (SGNMs) with distributed delays when the system parameters and external input are grey numbers.<\/jats:p><\/jats:sec>Design\/methodology\/approach<\/jats:title>Firstly, by using the properties of grey matrix, M-matrix theory and Homeomorphic mapping, the existence and uniqueness of equilibrium point of the SGNMs were discussed. Secondly, by constructing a proper Lyapunov functional and using the average dwell time approach and inequality technique, the robust exponential stability of the SGNMs under restricted switching was studied. Finally, a numerical example is given to verify the effectiveness of the proposed results.<\/jats:p><\/jats:sec>Findings<\/jats:title>Sufficient conditions for the existence and uniqueness of equilibrium point of the SGNMs have been established; sufficient conditions for guaranteeing the robust stability of the SGNMs under restricted switching have been obtained.<\/jats:p><\/jats:sec>Originality\/value<\/jats:title>(1) Different from asymptotic stability, the exponential stability of SGNMs which include grey parameters and distributed time delays will be investigated in this paper, and the exponential convergence rate of the SGNMs can also be obtained; (2) the activation functions, self-feedback coefficients and interconnected matrices are with different forms in different subnetworks; and (3) the results obtained by LMIs approach are complicated, while the proposed sufficient conditions are straightforward, which are conducive to practical applications.<\/jats:p><\/jats:sec>","DOI":"10.1108\/gs-11-2021-0177","type":"journal-article","created":{"date-parts":[[2022,4,14]],"date-time":"2022-04-14T02:58:06Z","timestamp":1649905086000},"page":"879-896","source":"Crossref","is-referenced-by-count":0,"title":["Robust stability analysis of switched grey neural network models with distributed delays over C"],"prefix":"10.1108","volume":"12","author":[{"ORCID":"http:\/\/orcid.org\/0000-0003-3317-4093","authenticated-orcid":false,"given":"Lei","family":"Zhang","sequence":"first","affiliation":[]},{"ORCID":"http:\/\/orcid.org\/0000-0003-0228-4476","authenticated-orcid":false,"given":"Huanbin","family":"Xue","sequence":"additional","affiliation":[]},{"ORCID":"http:\/\/orcid.org\/0000-0002-2437-0212","authenticated-orcid":false,"given":"Zeying","family":"Li","sequence":"additional","affiliation":[]},{"ORCID":"http:\/\/orcid.org\/0000-0001-5005-534X","authenticated-orcid":false,"given":"Yong","family":"Wei","sequence":"additional","affiliation":[]}],"member":"140","published-online":{"date-parts":[[2022,4,14]]},"reference":[{"key":"key2022111506484488500_ref001","doi-asserted-by":"crossref","first-page":"1027","DOI":"10.1016\/j.neunet.2004.02.001","article-title":"An analysis of exponential stability of delayed neural networks with time varying delays","volume":"17","year":"2004","journal-title":"Neural Networks"},{"key":"key2022111506484488500_ref002","volume-title":"Nonnegative Matrices in Mathematical Sciences","year":"1979"},{"key":"key2022111506484488500_ref003","doi-asserted-by":"crossref","first-page":"207","DOI":"10.1016\/j.matcom.2019.05.011","article-title":"Robust stability of uncertain stochastic complex-valued neural networks with additive time-varying delays","volume":"171","year":"2020","journal-title":"Mathematics and Computers in Simulation"},{"key":"key2022111506484488500_ref004","doi-asserted-by":"crossref","first-page":"1257","DOI":"10.1109\/31.7600","article-title":"Cellular neural networks: theory","volume":"35","year":"1988","journal-title":"IEEE Transactions on Circuits and Systems"},{"key":"key2022111506484488500_ref005","doi-asserted-by":"crossref","first-page":"288","DOI":"10.1016\/S0167-6911(82)80025-X","article-title":"Control problems of grey systems","volume":"1","year":"1982","journal-title":"Systems and Control Letters"},{"key":"key2022111506484488500_ref006","article-title":"Synchronization in finite-\/fixed-time of delayed diffusive complex-valued neural networks with discontinuous activations","volume":"142","year":"2021","journal-title":"Chaos, Solitons and Fractals"},{"issue":"2","key":"key2022111506484488500_ref500","first-page":"57","article-title":"Study on improvement of token and arithmetic of interval grey numbers and its GM(1, 1) model","volume":"7","year":"2005","journal-title":"Engineering Science"},{"issue":"7","key":"key2022111506484488500_ref007","doi-asserted-by":"crossref","first-page":"354","DOI":"10.1109\/81.401145","article-title":"New conditions for global stability of neural networks with application to linear and quadratic programming problems","volume":"42","year":"1995","journal-title":"IEEE Transactions on Circuits and Systems I: Fundamental Theory and Applications"},{"key":"key2022111506484488500_ref008","doi-asserted-by":"crossref","first-page":"853","DOI":"10.1109\/TNNLS.2012.2195028","article-title":"Global stability of complex-valued recurrent neural networks with timedelays","volume":"23","year":"2012","journal-title":"IEEE Transactions on Neural Networks and Learning Systems"},{"key":"key2022111506484488500_ref009","doi-asserted-by":"crossref","first-page":"760","DOI":"10.1016\/j.apm.2007.12.006","article-title":"Robust stability analysis of static neural network with S-type distributed delays","volume":"33","year":"2009","journal-title":"Applied Mathematical Modelling"},{"key":"key2022111506484488500_ref010","doi-asserted-by":"crossref","first-page":"23","DOI":"10.1016\/j.fss.2017.12.001","article-title":"Global exponential convergence of fuzzy complex-valued neural networks with time-varying delays and impulsive effects","volume":"338","year":"2018","journal-title":"Fuzzy Sets and Systems"},{"key":"key2022111506484488500_ref011","doi-asserted-by":"crossref","first-page":"257","DOI":"10.1093\/imamci\/dnt038","article-title":"Switched exponential state estimation and robust stability for interval neural networks with the average dwell time","volume":"32","year":"2015","journal-title":"IMA Journal of Mathematical Control and Information"},{"key":"key2022111506484488500_ref012","doi-asserted-by":"crossref","first-page":"2827","DOI":"10.1080\/00207721.2015.1029570","article-title":"Passivity and robust synchronisation of switched interval coupled neural networks with time delay","volume":"47","year":"2016","journal-title":"International Journal of Systems Science"},{"key":"key2022111506484488500_ref013","doi-asserted-by":"crossref","first-page":"267","DOI":"10.1016\/j.apm.2006.12.002","article-title":"The foundation of the grey matrix and the grey input-output analysis","volume":"32","year":"2008","journal-title":"Applied Mathematical Modelling"},{"key":"key2022111506484488500_ref014","doi-asserted-by":"crossref","first-page":"2565","DOI":"10.1016\/j.neucom.2017.11.031","article-title":"Stability of switched memristive neural networks with impulse and stochastic disturbance","volume":"275","year":"2018","journal-title":"Neurocomputing"},{"issue":"2","key":"key2022111506484488500_ref015","doi-asserted-by":"crossref","first-page":"357","DOI":"10.1109\/TNNLS.2014.2379920","article-title":"Passivity of switched recurrent neural networks with time-varying delays","volume":"26","year":"2015","journal-title":"IEEE Transactions on Neural Networks and Learning Systems"},{"key":"key2022111506484488500_ref016","volume-title":"Switching in Systems and Control","year":"2003"},{"key":"key2022111506484488500_ref017","volume-title":"Advances in Grey Systems Research","year":"2010"},{"issue":"2","key":"key2022111506484488500_ref018","doi-asserted-by":"crossref","first-page":"915","DOI":"10.1007\/s11071-017-3702-z","article-title":"Global exponential stability of stochastic memristor-based complex-valued neural networks with time delays","volume":"90","year":"2017","journal-title":"Nonlinear Dynamics"},{"issue":"1","key":"key2022111506484488500_ref019","first-page":"108","article-title":"On spectral analysis and new research directions in grey system theory","volume":"32","year":"2020","journal-title":"The Journal of Grey System"},{"key":"key2022111506484488500_ref020","doi-asserted-by":"crossref","first-page":"293","DOI":"10.1016\/j.neucom.2015.02.024","article-title":"Exponential stability of a class of complex-valued neural networks with time-varying delays","volume":"164","year":"2015","journal-title":"Neurocomputing"},{"issue":"2","key":"key2022111506484488500_ref021","doi-asserted-by":"crossref","first-page":"331","DOI":"10.1109\/72.279195","article-title":"An analysis of the gamma memory in dynamic neural networks","volume":"5","year":"1994","journal-title":"IEEE Transactions on Neural Networks"},{"issue":"2","key":"key2022111506484488500_ref022","doi-asserted-by":"crossref","first-page":"553","DOI":"10.1007\/s11063-015-9428-3","article-title":"Exponential stability of switched time-varying delayed neural networks with all modes being unstable","volume":"43","year":"2016","journal-title":"Neural Processing Letters"},{"issue":"1","key":"key2022111506484488500_ref023","doi-asserted-by":"crossref","first-page":"84","DOI":"10.1109\/TNNLS.2014.2311099","article-title":"Existence and uniform stability analysis of fractional-order complex-valued neural networks with time delays","volume":"26","year":"2015","journal-title":"IEEE Transactions on Neural Networks and Learning Systems"},{"key":"key2022111506484488500_ref024","volume-title":"Large-scale Dynamic Systems: Stability and Structure","year":"1978"},{"issue":"1","key":"key2022111506484488500_ref025","doi-asserted-by":"crossref","first-page":"188","DOI":"10.1016\/j.cam.2005.10.029","article-title":"Stability analysis of Cohen-Grossberg neural network with both time-varying and continuously distributed delays","volume":"197","year":"2006","journal-title":"Journal of Computational and Applied Mathematics"},{"key":"key2022111506484488500_ref026","doi-asserted-by":"crossref","first-page":"1044","DOI":"10.1016\/j.neucom.2015.05.020","article-title":"Impulsive effects on stability of discrete-time complex-valued neural networks with both discrete and distributed time-varying delays","volume":"168","year":"2015","journal-title":"Neurocomputing"},{"key":"key2022111506484488500_ref027","doi-asserted-by":"crossref","first-page":"108","DOI":"10.1016\/j.neunet.2016.03.007","article-title":"Global exponential stability of complex-valued neural networks with both time-varying delays and impulsive effects","volume":"79","year":"2016","journal-title":"Neural Networks"},{"key":"key2022111506484488500_ref028","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/j.neunet.2016.04.012","article-title":"Global exponential stability of impulsive complex-valued neural networks with both asynchronous time-varying and continuously distributed delays","volume":"81","year":"2016","journal-title":"Neural Networks"},{"issue":"7","key":"key2022111506484488500_ref029","doi-asserted-by":"crossref","first-page":"915","DOI":"10.1007\/s10483-009-0710-x","article-title":"The p-moment exponential robust stability for stochastic systems with distributed delays and interval parameters","volume":"30","year":"2009","journal-title":"Applied Mathematics and Mechanics"},{"issue":"4","key":"key2022111506484488500_ref030","first-page":"820","article-title":"P-moment stability analysis of impulsive stochastic functional differential systems and its application in grey system","volume":"26","year":"2014","journal-title":"The Journal of Grey System"},{"issue":"1","key":"key2022111506484488500_ref031","first-page":"59","article-title":"Robust stability of grey neutral stochastic differential systems with impulsive effects","volume":"26","year":"2014","journal-title":"The Journal of Grey System"},{"issue":"9","key":"key2022111506484488500_ref032","doi-asserted-by":"crossref","first-page":"1396","DOI":"10.1109\/TNN.2010.2056383","article-title":"Exponential stability analysis for delayed neural networks with switching parameters: average dwell time approach","volume":"21","year":"2010","journal-title":"IEEE Transactions on Neural Networks"},{"issue":"6","key":"key2022111506484488500_ref033","doi-asserted-by":"crossref","first-page":"1522","DOI":"10.1109\/TSMCB.2011.2157140","article-title":"Delay-dependent stability analysis for switched neural networks with time-varying delay","volume":"41","year":"2011","journal-title":"IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics)"},{"key":"key2022111506484488500_ref034","doi-asserted-by":"crossref","first-page":"38","DOI":"10.1016\/j.neucom.2018.03.046","article-title":"New results for uncertain switched neural networks with mixed delays using hybrid division method","volume":"307","year":"2018","journal-title":"Neurocomputing"},{"key":"key2022111506484488500_ref035","first-page":"839","article-title":"Stochastic exponential robust stability of delayed complex-valued neural networks with Markova jumping parameters","volume":"6","year":"2017","journal-title":"IEEE Access"},{"issue":"4","key":"key2022111506484488500_ref036","doi-asserted-by":"crossref","first-page":"686","DOI":"10.1080\/00207721.2016.1206988","article-title":"Dynamical behaviour analysis of delayed complex-valued neural networks with impulsive effect","volume":"48","year":"2017","journal-title":"International Journal of Systems Science"},{"key":"key2022111506484488500_ref037","article-title":"Robust exponential stability of switched complex-valued neural networks with interval parameter uncertainties and impulses","volume":"2018","year":"2018","journal-title":"Complexity"},{"key":"key2022111506484488500_ref038","article-title":"Robust exponential stability analysis of switched neural networks with interval parameter uncertainties and time delays","volume":"2018","year":"2018","journal-title":"Complexity"},{"issue":"16","key":"key2022111506484488500_ref039","first-page":"206","article-title":"Robust exponential stability of switched neural networks systems with unbounded delay","volume":"47","year":"2017","journal-title":"Journal of Mathematics in Practice and Theory"},{"issue":"1","key":"key2022111506484488500_ref040","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1109\/TFUZZ.2020.3029633","article-title":"Maximum-amplitude solution of addition-min fuzzy relation inequalities considering the stability in the P2P network system","volume":"30","year":"2022","journal-title":"IEEE Transactions on Fuzzy Systems"},{"key":"key2022111506484488500_ref041","doi-asserted-by":"crossref","first-page":"1316","DOI":"10.1007\/s11424-017-6092-x","article-title":"Robust exponential stability of switched interval interconnected systems with unbounded delay","volume":"30","year":"2017","journal-title":"Journal of Systems Science and Complexity"},{"key":"key2022111506484488500_ref042","doi-asserted-by":"crossref","first-page":"679","DOI":"10.1007\/s11071-019-05006-5","article-title":"Robust exponential stability of interconnected switched systems with mixed delays and impulsive effect","volume":"97","year":"2019","journal-title":"Nonlinear Dynamics"},{"issue":"5","key":"key2022111506484488500_ref043","article-title":"Robust exponential stability of large-scale system with mixed input delays and impulsive effect","volume":"11","year":"2016","journal-title":"Journal of Computational and Nonlinear Dynamics"},{"key":"key2022111506484488500_ref044","doi-asserted-by":"crossref","first-page":"456","DOI":"10.1016\/j.amc.2019.04.063","article-title":"Robust stability of impulsive switched neural networks with multiple time delays","volume":"359","year":"2019","journal-title":"Applied Mathematics and Computation"},{"key":"key2022111506484488500_ref045","doi-asserted-by":"crossref","first-page":"813","DOI":"10.1016\/j.neucom.2019.11.120","article-title":"Robust stability analysis of stochastic switched neural networks with parameter uncertainties via state-dependent switching law","volume":"452","year":"2021","journal-title":"Neurocomputing"},{"key":"key2022111506484488500_ref046","doi-asserted-by":"crossref","first-page":"248","DOI":"10.1016\/j.neunet.2019.12.012","article-title":"Existence and finite-time stability of discrete fractional-order complex-valued neural networks with time delays","volume":"123","year":"2020","journal-title":"Neural Networks"},{"issue":"3","key":"key2022111506484488500_ref047","doi-asserted-by":"crossref","first-page":"391","DOI":"10.1016\/j.neunet.2003.09.005","article-title":"Absolutely exponential stability of a class of neural networks with unbounded delay","volume":"17","year":"2004","journal-title":"Neural Networks"},{"key":"key2022111506484488500_ref048","article-title":"Robust stability analysis of fuzzy neural network with delays","volume":"2009","year":"2009","journal-title":"Mathematical Problems in Engineering"},{"issue":"1","key":"key2022111506484488500_ref049","doi-asserted-by":"crossref","first-page":"313","DOI":"10.1080\/00207178608933466","article-title":"The stability of the grey linear system","volume":"43","year":"1986","journal-title":"International Journal of Control"},{"issue":"2","key":"key2022111506484488500_ref050","doi-asserted-by":"crossref","first-page":"173","DOI":"10.1109\/9.21090","article-title":"Stability analysis of gray discrete-time systems","volume":"34","year":"1989","journal-title":"IEEE Transactions on Automatic Control"}],"container-title":["Grey Systems: Theory and Application"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.emerald.com\/insight\/content\/doi\/10.1108\/GS-11-2021-0177\/full\/xml","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.emerald.com\/insight\/content\/doi\/10.1108\/GS-11-2021-0177\/full\/html","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2022,11,15]],"date-time":"2022-11-15T06:49:45Z","timestamp":1668494985000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.emerald.com\/insight\/content\/doi\/10.1108\/GS-11-2021-0177\/full\/html"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,4,14]]},"references-count":51,"journal-issue":{"issue":"4","published-online":{"date-parts":[[2022,4,14]]},"published-print":{"date-parts":[[2022,11,16]]}},"alternative-id":["10.1108\/GS-11-2021-0177"],"URL":"https:\/\/doi.org\/10.1108\/gs-11-2021-0177","relation":{},"ISSN":["2043-9377"],"issn-type":[{"value":"2043-9377","type":"print"}],"subject":[],"published":{"date-parts":[[2022,4,14]]}}}