caa a22 4500 606199667 CHVBK 20210128100939.0 cr unu---uuuuu 210128e20150401xx s 000 0 eng 10.1007/s11045-014-0297-0 doi (NATIONALLICENCE)springer-10.1007/s11045-014-0297-0 Notes on minimal realizations of multidimensional systems [Elektronische Daten] [Minh Doan, Thanh Nguyen, Zhiping Lin, Li Xu] In this paper, we formalize two related but different notions for state-space realization of multidimensional ( $$n\hbox {D}$$ n D ) single-input-single-output discrete systems in $$n\hbox {D}$$ n D Roesser model, namely the "absolutely minimal realization” and the "minimal realization”. We then focus our study mainly on first-degree 2D and 3D causal systems. A necessary and sufficient condition for absolutely minimal realizations is given for first-degree 2D systems. It is then shown that first-degree 2D systems that do not admit absolutely minimal realizations always admit minimal realizations of order 3. A Gröbner basis approach is also proposed which leads to a sufficient condition for the absolutely minimal realizations of some higher-degree 2D systems. We then present a symbolic method that gives simple necessary conditions for the existence of absolutely minimal realizations for first-degree 3D systems. A two-step approach to absolutely minimal realizations for first-degree 3D systems is then presented, followed by techniques for minimal realizations of first-degree 3D systems. Throughout the paper, several non-trivial examples are illustrated with the aim of helping the reader to apply the realization methods proposed in this paper. Springer Science+Business Media New York, 2014 Multidimensional systems nationallicence State-space realization nationallicence Minimal realization nationallicence Roesser model nationallicence Symbolic approach nationallicence Gröbner basis nationallicence Doan Minh School of Physics and Mathematics Sciences, Nanyang Technological University, Singapore, Singapore aut Nguyen Thanh School of Physics and Mathematics Sciences, Nanyang Technological University, Singapore, Singapore aut Lin Zhiping School of Electrical and Electronic Engineering, Nanyang Technological University, Singapore, Singapore aut Xu Li Department of Electronics and Information Systems, Akita Prefectural University, Akita, Japan aut Multidimensional Systems and Signal Processing Springer US; http://www.springer-ny.com 26/2(2015-04-01), 519-553 0923-6082 26:2<519 2015 26 11045 https://doi.org/10.1007/s11045-014-0297-0 text/html Onlinezugriff via DOI BK010053 XK010053 XK010000 Metadata rights reserved Springer special CC-BY-NC licence nationallicence 1 research-article jats NATIONALLICENCE NATIONALLICENCE NL-springer NATIONALLICENCE 856 40 https://doi.org/10.1007/s11045-014-0297-0 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Doan Minh School of Physics and Mathematics Sciences, Nanyang Technological University, Singapore, Singapore aut NATIONALLICENCE 700 1- Nguyen Thanh School of Physics and Mathematics Sciences, Nanyang Technological University, Singapore, Singapore aut NATIONALLICENCE 700 1- Lin Zhiping School of Electrical and Electronic Engineering, Nanyang Technological University, Singapore, Singapore aut NATIONALLICENCE 700 1- Xu Li Department of Electronics and Information Systems, Akita Prefectural University, Akita, Japan aut NATIONALLICENCE 773 0- Multidimensional Systems and Signal Processing Springer US; http://www.springer-ny.com 26/2(2015-04-01), 519-553 0923-6082 26:2<519 2015 26 11045