{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,31]],"date-time":"2026-01-31T01:00:34Z","timestamp":1769821234878,"version":"3.49.0"},"reference-count":46,"publisher":"MDPI AG","issue":"6","license":[{"start":{"date-parts":[[2020,6,20]],"date-time":"2020-06-20T00:00:00Z","timestamp":1592611200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100004705","name":"King Mongkut's University of Technology Thonburi","doi-asserted-by":"publisher","award":["King Mongkut's University of Technology Thonburi"],"award-info":[{"award-number":["King Mongkut's University of Technology Thonburi"]}],"id":[{"id":"10.13039\/501100004705","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>The main focus of this research is on a comprehensive analysis of robust dissipativity issues pertaining to a class of uncertain stochastic generalized neural network (USGNN) models in the presence of time-varying delays and Markovian jumping parameters (MJPs). In real-world environments, most practical systems are subject to uncertainties. As a result, we take the norm-bounded parameter uncertainties, as well as stochastic disturbances into consideration in our study. To address the task, we formulate the appropriate Lyapunov\u2013Krasovskii functional (LKF), and through the use of effective integral inequalities, simplified linear matrix inequality (LMI) based sufficient conditions are derived. We validate the feasible solutions through numerical examples using MATLAB software. The simulation results are analyzed and discussed, which positively indicate the feasibility and effectiveness of the obtained theoretical findings.<\/jats:p>","DOI":"10.3390\/sym12061035","type":"journal-article","created":{"date-parts":[[2020,6,24]],"date-time":"2020-06-24T07:14:19Z","timestamp":1592982859000},"page":"1035","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":20,"title":["An Extended Analysis on Robust Dissipativity of Uncertain Stochastic Generalized Neural Networks with Markovian Jumping Parameters"],"prefix":"10.3390","volume":"12","author":[{"given":"Usa","family":"Humphries","sequence":"first","affiliation":[{"name":"Department of Mathematics, Faculty of Science, King Mongkut\u2019s University of Technology Thonburi (KMUTT), Thung Khru 10140, Thailand"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6053-6219","authenticated-orcid":false,"given":"Grienggrai","family":"Rajchakit","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Faculty of Science, Maejo University, Chiang Mai 50290, Thailand"}]},{"given":"Ramalingam","family":"Sriraman","sequence":"additional","affiliation":[{"name":"Department of Science and Humanities, Vel Tech High Tech Dr. Rangarajan Dr. Sakunthala Engineering College, Avadi, Tamil Nadu 600062, India"}]},{"given":"Pramet","family":"Kaewmesri","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Faculty of Science, King Mongkut\u2019s University of Technology Thonburi (KMUTT), Thung Khru 10140, Thailand"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0130-9304","authenticated-orcid":false,"given":"Pharunyou","family":"Chanthorn","sequence":"additional","affiliation":[{"name":"Research Center in Mathematics and Applied Mathematics, Department of Mathematics, Faculty of Science, Chiang Mai University, Chiang Mai 50200, Thailand"}]},{"given":"Chee Peng","family":"Lim","sequence":"additional","affiliation":[{"name":"Institute for Intelligent Systems Research and Innovation, Deakin University, Waurn Ponds, VIC 3216, Australia"}]},{"given":"Rajendran","family":"Samidurai","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Thiruvalluvar University, Vellore, Tamil Nadu 632115, India"}]}],"member":"1968","published-online":{"date-parts":[[2020,6,20]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"1313","DOI":"10.1080\/00207720050165807","article-title":"Global asymptotic stability of neural networks with transmission delays","volume":"31","author":"Cao","year":"2000","journal-title":"Int. J. Syst. Sci."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"1239","DOI":"10.1109\/TNN.2002.1031957","article-title":"An analysis of global asymptotic stability of delayed cellular neural networks","volume":"13","author":"Arik","year":"2012","journal-title":"IEEE Trans. Neural Netw."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"22","DOI":"10.1016\/j.neucom.2012.08.049","article-title":"Passivity analysis of stochastic neural networks with time-varying delays and leakage delay","volume":"125","author":"Zhao","year":"2014","journal-title":"Neurocomputing"},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"213","DOI":"10.1007\/s13042-014-0257-x","article-title":"State estimation for memristor-based neural networks with time-varying delays","volume":"6","author":"Wei","year":"2015","journal-title":"Int. J. Mach. Learn. Cybern."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"5606","DOI":"10.1109\/TNNLS.2018.2806356","article-title":"Reduced-order filtering of delayed static neural networks with Markovian jumping parameters","volume":"29","author":"Huang","year":"2018","journal-title":"IEEE Trans. Neural Netw. Learn. Syst."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"1006","DOI":"10.1016\/j.isatra.2014.05.002","article-title":"Robust stochastic stability of discrete-time fuzzy Markovian jump neural networks","volume":"53","author":"Arunkumar","year":"2014","journal-title":"ISA Trans."},{"key":"ref_7","first-page":"869","article-title":"Stochastic stability for distributed delay neural networks via augmented Lyapunov\u2013Krasovskii functionals","volume":"338","author":"Chen","year":"2018","journal-title":"Appl. Math. Comput."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"2137","DOI":"10.1016\/j.jfranklin.2016.02.020","article-title":"Delay-dependent stability and dissipativity analysis of generalized neural networks with Markovian jump parameters and two delay components","volume":"353","author":"Chen","year":"2016","journal-title":"J. Frankl. Inst."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"485","DOI":"10.1109\/TSMC.2016.2609147","article-title":"New criteria for stability of generalized neural networks including Markov jump parameters and additive time delays","volume":"48","author":"Samidurai","year":"2018","journal-title":"IEEE Trans. Syst. Man Cybern. Syst."},{"key":"ref_10","first-page":"338","article-title":"Further results on dissipativity and stability analysis of Markov jump generalized neural networks with time-varying interval delays","volume":"336","author":"Jiao","year":"2018","journal-title":"Appl. Math. Comput."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"1263","DOI":"10.1109\/TNNLS.2013.2284968","article-title":"Delay-dependent stability criteria for generalized neural networks with two delay components","volume":"25","author":"Zhang","year":"2014","journal-title":"IEEE Trans. Neural Netw. Learn. Syst."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"148","DOI":"10.1016\/j.neucom.2015.02.055","article-title":"Stability analysis of generalized neural networks with time-varying delays via a new integral inequality","volume":"161","author":"Zeng","year":"2015","journal-title":"Neurocomputing"},{"key":"ref_13","first-page":"322","article-title":"New criteria of stability analysis for generalized neural networks subject to time-varying delayed signals","volume":"314","author":"Wang","year":"2017","journal-title":"Appl. Math. Comput."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"103","DOI":"10.1016\/j.matcom.2019.04.001","article-title":"Global asymptotic stability of stochastic complex-valued neural networks with probabilistic time-varying delays","volume":"171","author":"Sriraman","year":"2020","journal-title":"Math. Comput. Simulat."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"2174","DOI":"10.1016\/j.jfranklin.2011.06.010","article-title":"Delay-dependent non-fragile robust stabilization and H\u221e control of uncertain stochastic systems with time-varying delay and nonlinearity","volume":"348","author":"Wang","year":"2011","journal-title":"J. Frankl. Inst."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"201","DOI":"10.1016\/j.matcom.2018.03.010","article-title":"Robust dissipativity analysis for uncertain neural networks with additive time-varying delays and general activation functions","volume":"155","author":"Samidurai","year":"2019","journal-title":"Math. Comput. Simulat."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"329","DOI":"10.1080\/00207170010008752","article-title":"Delay-dependent robust stability and H\u221e control of jump linear systems with time-delay","volume":"74","author":"Boukas","year":"2010","journal-title":"Int. J. Control"},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"423","DOI":"10.1016\/j.jfranklin.2003.09.001","article-title":"Delay-dependent stochastic stability and H\u221e analysis for time-delay systems with Markovian jumping parameters","volume":"340","author":"Cao","year":"2013","journal-title":"J. Frankl. Inst."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"341","DOI":"10.1109\/TSMCB.2010.2053354","article-title":"Exponential stability of stochastic neural networks with both Markovian jump parameters and mixed time delays","volume":"41","author":"Zhu","year":"2011","journal-title":"IEEE Trans. Syst. Man Cybern. Part B"},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"864","DOI":"10.1016\/j.neucom.2014.10.009","article-title":"Stability analysis of stochastic Markovian switching static neural networks with asynchronous mode-dependent delays","volume":"151","author":"Tan","year":"2015","journal-title":"Neurocomputing"},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"245","DOI":"10.1016\/j.neucom.2017.04.004","article-title":"Robust input-to-state stability of neural networks with Markovian switching in presence of random disturbances or time delays","volume":"249","author":"Zhu","year":"2017","journal-title":"Neurocomputing"},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"481","DOI":"10.1016\/S0016-0032(01)00016-3","article-title":"Stability of stochastic delay neural networks","volume":"338","author":"Blythe","year":"2001","journal-title":"J. Frankl. Inst."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"2122","DOI":"10.1109\/TCYB.2013.2240451","article-title":"Stability analysis of time-delay neural networks subject to stochastic perturbations","volume":"43","author":"Chen","year":"2013","journal-title":"IEEE Trans. Cybern."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"467","DOI":"10.1109\/TSMCB.2008.2006860","article-title":"Novel robust stability criteria for stochastic Hopfield neural networks with time delays","volume":"39","author":"Yang","year":"2009","journal-title":"IEEE Trans. Syst. Man Cybern. Part B"},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"1754","DOI":"10.1016\/j.neucom.2011.02.010","article-title":"Passivity analysis of stochastic delayed neural networks with Markovian switching","volume":"74","author":"Zhu","year":"2011","journal-title":"Neurocomputing"},{"key":"ref_26","first-page":"189","article-title":"Stability and dissipativity analysis for neutral type stochastic Markovian jump static neural networks with time delays","volume":"9","author":"Cao","year":"2019","journal-title":"J. Artif. Int. Soft Comput. Res."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"349","DOI":"10.1007\/s00521-011-0696-1","article-title":"Robust stability criteria for uncertain stochastic neural networks of neutral-type with interval time-varying delays","volume":"22","author":"Liu","year":"2013","journal-title":"Neural Comput. Appl."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"59","DOI":"10.1002\/cplx.21630","article-title":"Robust stability analysis of stochastic neural networks with Markovian jumping parameters and probabilistic time-varying delays","volume":"21","author":"Pradeep","year":"2014","journal-title":"Complexity"},{"key":"ref_29","first-page":"213","article-title":"Robust passivity analysis of fuzzy Cohen-Grossberg BAM neural networks with time-varying delays","volume":"275","author":"Sakthivel","year":"2011","journal-title":"Appl. Math. Comput."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"1232","DOI":"10.1016\/j.physleta.2010.01.007","article-title":"Improved delay-dependent exponential stability for uncertain stochastic neural networks with time-varying delays","volume":"374","author":"Kwon","year":"2010","journal-title":"Phys. Lett. A"},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"4091","DOI":"10.1016\/j.jfranklin.2016.07.006","article-title":"Robust finite time stabilization analysis for uncertain neural networks with leakage delay and probabilistic time-varying delays","volume":"353","author":"Muthukumar","year":"2016","journal-title":"J. Frankl. Inst."},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"2290","DOI":"10.1007\/s12555-017-0720-z","article-title":"Stability and stabilization criteria for sampled-data control system via augmented Lyapunov\u2013Krasovskii functionals","volume":"16","author":"Lee","year":"2018","journal-title":"Int. J. Control. Autom. Syst."},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"6531","DOI":"10.1016\/j.jfranklin.2018.06.023","article-title":"Enhanced stability criteria of neural networks with time-varying delays via a generalized free-weighting matrix integral inequality","volume":"355","author":"Park","year":"2018","journal-title":"J. Frankl. Inst."},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"321","DOI":"10.1007\/BF00276493","article-title":"Dissipative dynamical systems part I: General theory","volume":"45","author":"Willems","year":"1972","journal-title":"Arch. Ration. Mech. Anal."},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"327","DOI":"10.1016\/0016-0032(80)90026-5","article-title":"Dissipative dynamical systems: Basic input-output and state properties","volume":"309","author":"Hill","year":"1980","journal-title":"J. Frankl. Inst."},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"1323","DOI":"10.1007\/s11071-012-0350-1","article-title":"Robust dissipativity analysis of neural networks with time-varying delay and randomly occurring uncertainties","volume":"69","author":"Wu","year":"2012","journal-title":"Nonlinear Dyn."},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"016118","DOI":"10.1103\/PhysRevE.68.016118","article-title":"Global dissipativity of continuous-time recurrent neural networks with time delay","volume":"68","author":"Liao","year":"2013","journal-title":"Phys. Rev. E"},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"393","DOI":"10.1016\/j.chaos.2004.11.035","article-title":"Global dissipativity of neural networks with both variable and unbounded delays","volume":"25","author":"Song","year":"2005","journal-title":"Chaos Solitons Fract."},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"976","DOI":"10.1109\/TNN.2011.2128341","article-title":"Stability and dissipativity analysis of distributed delay cellular neural networks","volume":"22","author":"Feng","year":"2011","journal-title":"IEEE Trans. Neural Netw."},{"key":"ref_40","doi-asserted-by":"crossref","first-page":"3217","DOI":"10.1016\/j.jfranklin.2013.08.003","article-title":"Dissipativity of discrete-time BAM stochastic neural networks with Markovian switching and impulses","volume":"350","author":"Raja","year":"2013","journal-title":"J. Frankl. Inst."},{"key":"ref_41","doi-asserted-by":"crossref","first-page":"1284","DOI":"10.1016\/j.jfranklin.2014.12.023","article-title":"Stability and dissipativity analysis of static neural networks with interval time-varying delay","volume":"352","author":"Zeng","year":"2015","journal-title":"J. Frankl. Inst."},{"key":"ref_42","doi-asserted-by":"crossref","first-page":"013105","DOI":"10.1063\/1.2126940","article-title":"Global point dissipativity of neural networks with mixed time-varying delays","volume":"16","author":"Cao","year":"2006","journal-title":"Chaos"},{"key":"ref_43","doi-asserted-by":"crossref","first-page":"98","DOI":"10.1016\/j.neucom.2017.12.044","article-title":"New results on stability analysis of delayed systems derived from extended Wirtingers integral inequality","volume":"283","author":"Zhang","year":"2018","journal-title":"Neurocomputing"},{"key":"ref_44","doi-asserted-by":"crossref","first-page":"4335","DOI":"10.1016\/j.jfranklin.2018.11.046","article-title":"Non-fragile sampled-data stabilization analysis for linear systems with probabilistic time-varying delays","volume":"356","author":"Samidurai","year":"2019","journal-title":"J. Frankl. Inst."},{"key":"ref_45","doi-asserted-by":"crossref","unstructured":"Gu, K., Kharitonov, V.L., and Chen, J. (2003). Stability of Time-Delay Systems, Birkh\u00e4user.","DOI":"10.1007\/978-1-4612-0039-0"},{"key":"ref_46","doi-asserted-by":"crossref","first-page":"1314","DOI":"10.1109\/TNN.2010.2054108","article-title":"Robust exponential stability of Markovian jump impulsive stochastic Cohen-Grossberg neural networks with mixed time delays","volume":"21","author":"Zhu","year":"2010","journal-title":"IEEE Trans. Neural Netw."}],"container-title":["Symmetry"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2073-8994\/12\/6\/1035\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T09:41:07Z","timestamp":1760175667000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2073-8994\/12\/6\/1035"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,6,20]]},"references-count":46,"journal-issue":{"issue":"6","published-online":{"date-parts":[[2020,6]]}},"alternative-id":["sym12061035"],"URL":"https:\/\/doi.org\/10.3390\/sym12061035","relation":{},"ISSN":["2073-8994"],"issn-type":[{"value":"2073-8994","type":"electronic"}],"subject":[],"published":{"date-parts":[[2020,6,20]]}}}