{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,7]],"date-time":"2026-07-07T10:37:38Z","timestamp":1783420658985,"version":"3.54.6"},"reference-count":43,"publisher":"MDPI AG","issue":"9","license":[{"start":{"date-parts":[[2014,9,15]],"date-time":"2014-09-15T00:00:00Z","timestamp":1410739200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/3.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>In a previous study we provided analytical and experimental evidence that some materials are able to store entropy-flow, of which the heat-conduction behaves as standing waves in a bounded region small enough in practice. In this paper we continue to develop distributed control of heat conduction in these thermal-inductive materials. The control objective is to achieve subtle temperature distribution in space and simultaneously to suppress its transient overshoots in time. This technology concerns safe and accurate heating\/cooling treatments in medical operations, polymer processing, and other prevailing modern day practices. Serving for distributed feedback, spatiotemporal H \u221e \/\u03bc control is developed by expansion of the conventional 1D-H \u221e \/\u03bc control to a 2D version. Therein 2D geometrical isomorphism is constructed with the Laplace-Galerkin transform, which extends the small-gain theorem into the mode-frequency domain, wherein 2D transfer-function controllers are synthesized with graphical methods. Finally, 2D digital-signal processing is programmed to implement 2D transfer-function controllers, possibly of spatial fraction-orders, into DSP-engine embedded microcontrollers.<\/jats:p>","DOI":"10.3390\/e16094937","type":"journal-article","created":{"date-parts":[[2014,9,15]],"date-time":"2014-09-15T10:31:10Z","timestamp":1410777070000},"page":"4937-4959","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["Distributed Control of Heat Conduction in Thermal Inductive Materials with 2D Geometrical Isomorphism"],"prefix":"10.3390","volume":"16","author":[{"given":"Chia-Yu","family":"Chou","sequence":"first","affiliation":[{"name":"Department of Mechanical Engineering, National Chung Cheng University, Chia-Yi 62102, Taiwan"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Boe-Shong","family":"Hong","sequence":"additional","affiliation":[{"name":"Department of Mechanical Engineering, National Chung Cheng University, Chia-Yi 62102, Taiwan"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Pei-Ju","family":"Chiang","sequence":"additional","affiliation":[{"name":"Department of Mechanical Engineering, National Chung Cheng University, Chia-Yi 62102, Taiwan"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Wen-Teng","family":"Wang","sequence":"additional","affiliation":[{"name":"Department of Mechanical and Computer-Aided Engineering, National Formosa University, Yunlin 63201, Taiwan"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Liang-Kuang","family":"Chen","sequence":"additional","affiliation":[{"name":"Department of Mechanical Engineering, National Taiwan University of Science and Technology, Taipei 10607, Taiwan"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Chia-Yen","family":"Lee","sequence":"additional","affiliation":[{"name":"Department of Vehicle Engineering, National Pingtung University of Science and Technology, Pingtung 91201, Taiwan"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2014,9,15]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"1101","DOI":"10.3390\/e16021101","article-title":"Realization of thermal inertia in frequency domain","volume":"16","author":"Hong","year":"2014","journal-title":"Entropy"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"4031","DOI":"10.1016\/j.apm.2011.02.021","article-title":"Realization of non-Fourier phenomena in heat transfer with 2D transfer function","volume":"35","author":"Hong","year":"2011","journal-title":"Appl. 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