{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T01:04:03Z","timestamp":1760058243000,"version":"build-2065373602"},"reference-count":52,"publisher":"MDPI AG","issue":"3","license":[{"start":{"date-parts":[[2025,3,19]],"date-time":"2025-03-19T00:00:00Z","timestamp":1742342400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>The present paper elaborates on the development of a theory of discrete-time dynamical systems on finite-dimensional structured state spaces. Dynamical systems on structured state spaces possess well-known applications to solving differential equations in physics, and it was shown that discrete-time systems on finite- (albeit high-) dimensional structured state spaces possess solid applications to structured signal processing and nonlinear system identification, modeling and control. With reference to the state-space representation of dynamical systems, the present contribution tackles the core system-theoretic problem of determining suitable laws to express a system\u2019s state transition. In particular, the present contribution aims at formulating a fairly general class of state-transition laws over the Lie algebra associated to a Lie group and at extending some properties of classical dynamical systems to process Lie-algebra-valued state signals.<\/jats:p>","DOI":"10.3390\/sym17030463","type":"journal-article","created":{"date-parts":[[2025,3,20]],"date-time":"2025-03-20T07:59:54Z","timestamp":1742457594000},"page":"463","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["Discrete-Time Dynamical Systems on Structured State Spaces: State-Transition Laws in Finite-Dimensional Lie Algebras"],"prefix":"10.3390","volume":"17","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-5964-7464","authenticated-orcid":false,"given":"Simone","family":"Fiori","sequence":"first","affiliation":[{"name":"Dipartimento di Ingegneria dell\u2019Informazione, Universit\u00e0 Politecnica delle Marche, Via Brecce Bianche, I-60131 Ancona, Italy"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2025,3,19]]},"reference":[{"key":"ref_1","unstructured":"Hsu, P. 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