{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,11,4]],"date-time":"2025-11-04T05:23:03Z","timestamp":1762233783489,"version":"build-2065373602"},"reference-count":41,"publisher":"MDPI AG","issue":"11","license":[{"start":{"date-parts":[[2025,10,30]],"date-time":"2025-10-30T00:00:00Z","timestamp":1761782400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"crossref","award":["62163008","61763004"],"award-info":[{"award-number":["62163008","61763004"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"crossref"}]},{"name":"Qiankehe Platform","award":["ZSYS[2025]007"],"award-info":[{"award-number":["ZSYS[2025]007"]}]},{"name":"Guizhou Provincial Science and Technology Projects","award":["[2020]1Z054"],"award-info":[{"award-number":["[2020]1Z054"]}]},{"name":"PhD start-up fund of Guizhou Institute of Technology","award":["XJGC20150411"],"award-info":[{"award-number":["XJGC20150411"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>Controllers designed on the basis of an approximate discrete time model can fail when they are applied to the real processes. This is a problem of interest in adaptive symmetry control system theory. In this paper, we introduce the certain polynomial for discretizing the n-th order integrator in the case of a fractional-order hold (FROH) and delta operator. Moreover, the corresponding FROH discretization pulse transfer function and sampling data model in normal form are derived. On the basis of these results, we present FROH discrete system zero dynamics and sampling zero dynamics where their asymptotic symmetry properties are obtained. In addition, the implications incorporating sampling zero dynamics in the discrete-time models used for system identification become evident as the sampling period approaches zero. It is a further extension of the corresponding results.<\/jats:p>","DOI":"10.3390\/sym17111826","type":"journal-article","created":{"date-parts":[[2025,10,31]],"date-time":"2025-10-31T02:48:28Z","timestamp":1761878908000},"page":"1826","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Asymptotic Symmetry Behavior for a Sampled Data Model via Fractional-Order Hold and Delta Operators"],"prefix":"10.3390","volume":"17","author":[{"given":"Nan","family":"Chi","sequence":"first","affiliation":[{"name":"College of Science, Guizhou Institute of Technology, Guiyang 550003, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8721-6178","authenticated-orcid":false,"given":"Cheng","family":"Zeng","sequence":"additional","affiliation":[{"name":"College of Science, Guizhou Institute of Technology, Guiyang 550003, China"},{"name":"The Key Laboratory of New Power System Operation Control of Guizhou Province, Guiyang 550003, China"},{"name":"Special Key Laboratory of Artificial Intelligence and Intelligent Control of Guizhou Province, Guiyang 550003, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2025,10,30]]},"reference":[{"key":"ref_1","unstructured":"\u00c5str\u00f6m, K.J., and Wittenmark, B. 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