{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,11,18]],"date-time":"2025-11-18T05:15:12Z","timestamp":1763442912714,"version":"3.45.0"},"reference-count":36,"publisher":"MDPI AG","issue":"11","license":[{"start":{"date-parts":[[2025,11,15]],"date-time":"2025-11-15T00:00:00Z","timestamp":1763164800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100021171","name":"Guangdong basic and applied basic research foundation","doi-asserted-by":"crossref","award":["2025A1515010466"],"award-info":[{"award-number":["2025A1515010466"]}],"id":[{"id":"10.13039\/501100021171","id-type":"DOI","asserted-by":"crossref"}]},{"name":"Guangdong Key Construction Discipline Scientific Research Ability Enhancement Project","award":["2024ZDJS056"],"award-info":[{"award-number":["2024ZDJS056"]}]},{"name":"Guangzhou Programs","award":["2024312151","2024312000","2024312374"],"award-info":[{"award-number":["2024312151","2024312000","2024312374"]}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"crossref","award":["11561029"],"award-info":[{"award-number":["11561029"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"crossref"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>Various types of noise interference often challenge the solution of discrete time-varying linear matrix problems with boundary constraints in practical engineering applications. To address this issue, this paper proposes a Taylor-type direct-discrete-time integral noise-immune recurrent neural network (TD-IRNN) model. Specifically, the model is constructed by transforming the bounded discrete linear matrix problem into a unified discrete matrix formulation and incorporating an error accumulation term during the design process. The proposed TD-IRNN model not only eliminates the need for continuous-environment conversion but also significantly enhances its noise immunity. Theoretical analysis demonstrates that the model exhibits excellent convergence and stability under different noise conditions. Numerical experiments and a robotic manipulator trajectory tracking experiment further validate the effectiveness and practical applicability of the TD-IRNN model in complex environments.<\/jats:p>","DOI":"10.3390\/sym17111975","type":"journal-article","created":{"date-parts":[[2025,11,17]],"date-time":"2025-11-17T14:04:07Z","timestamp":1763388247000},"page":"1975","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Taylor-Type Direct-Discrete-Time Integral Recurrent Neural Network with Noise Tolerance for Discrete-Time-Varying Linear Matrix Problems with Symmetric Boundary Constraints"],"prefix":"10.3390","volume":"17","author":[{"given":"Yuhuan","family":"Chen","sequence":"first","affiliation":[{"name":"School of Artificial Intelligence, Guangzhou Maritime University, Guangzhou 510275, China"}]},{"given":"Xuan","family":"Li","sequence":"additional","affiliation":[{"name":"School of Cyber Security, Guangdong Polytechnic Normal University, Guangzhou 510635, China"}]},{"given":"Jie","family":"Chen","sequence":"additional","affiliation":[{"name":"School of Cyber Security, Guangdong Polytechnic Normal University, Guangzhou 510635, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-0478-719X","authenticated-orcid":false,"given":"Chenfu","family":"Yi","sequence":"additional","affiliation":[{"name":"School of Cyber Security, Guangdong Polytechnic Normal University, Guangzhou 510635, China"},{"name":"School of Information Engineering, Jiangxi University of Science and Technology, Ganzhou 341000, China"}]},{"given":"Yang","family":"Li","sequence":"additional","affiliation":[{"name":"School of Artificial Intelligence, Guangzhou Maritime University, Guangzhou 510275, China"}]}],"member":"1968","published-online":{"date-parts":[[2025,11,15]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"2004","DOI":"10.1109\/TAC.2024.3482119","article-title":"New Approach to Feedback Stabilization of Linear Discrete Time-Varying Stochastic Systems","volume":"70","author":"Zhang","year":"2025","journal-title":"IEEE Trans. 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