{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,20]],"date-time":"2026-06-20T09:46:35Z","timestamp":1781948795646,"version":"3.54.5"},"reference-count":41,"publisher":"Springer Science and Business Media LLC","issue":"3","license":[{"start":{"date-parts":[[2018,10,12]],"date-time":"2018-10-12T00:00:00Z","timestamp":1539302400000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"},{"start":{"date-parts":[[2018,10,12]],"date-time":"2018-10-12T00:00:00Z","timestamp":1539302400000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"funder":[{"name":"National Science Centre in Poland","award":["2015\/17\/B\/ST7\/03703"],"award-info":[{"award-number":["2015\/17\/B\/ST7\/03703"]}]},{"DOI":"10.13039\/501100001691","name":"Japan Society for the Promotion of Science","doi-asserted-by":"publisher","award":["JSPS.KAKENHI15K06072"],"award-info":[{"award-number":["JSPS.KAKENHI15K06072"]}],"id":[{"id":"10.13039\/501100001691","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Multidim Syst Sign Process"],"published-print":{"date-parts":[[2019,7]]},"DOI":"10.1007\/s11045-018-0619-8","type":"journal-article","created":{"date-parts":[[2018,10,12]],"date-time":"2018-10-12T07:44:48Z","timestamp":1539330288000},"page":"1583-1608","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":7,"title":["3-D modelling of rectangular circuits as the particular class of spatially interconnected systems on the plane"],"prefix":"10.1007","volume":"30","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-5305-1616","authenticated-orcid":false,"given":"Dongdong","family":"Zhao","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Krzysztof","family":"Galkowski","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Bartlomiej","family":"Sulikowski","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Li","family":"Xu","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","published-online":{"date-parts":[[2018,10,12]]},"reference":[{"issue":"7","key":"619_CR1","doi-asserted-by":"crossref","first-page":"1745","DOI":"10.1109\/TAC.2015.2398887","volume":"60","author":"CK Ahn","year":"2015","unstructured":"Ahn, C. K., Shi, P., & Basin, M. V. (2015). Two-dimensional dissipative control and filtering for roesser model. IEEE Transactions on Automatic Control, 60(7), 1745\u20131759.","journal-title":"IEEE Transactions on Automatic Control"},{"key":"619_CR2","volume-title":"A linear systems primer","author":"P\u00a0J Antsaklis","year":"2007","unstructured":"Antsaklis, P\u00a0. J., & Michel, A\u00a0. N. (2007). A linear systems primer (Vol. 1). Boston: Birkh\u00e4user."},{"issue":"10","key":"619_CR3","doi-asserted-by":"crossref","first-page":"1815","DOI":"10.1109\/TAC.2004.835582","volume":"49","author":"C Beck","year":"2004","unstructured":"Beck, C., & D\u2019Andrea, R. (2004). Noncommuting multidimensional realization theory: Minimality, reachability, and observability. IEEE Transactions on Automatic Control, 49(10), 1815\u20131822.","journal-title":"IEEE Transactions on Automatic Control"},{"key":"619_CR4","volume-title":"Multidimensional systems theory and applications","author":"N Bose","year":"2003","unstructured":"Bose, N., Buchberger, B., & Guiver, J. (2003). Multidimensional systems theory and applications. Dordrecht: Kluwer."},{"key":"619_CR5","volume-title":"Applied multidimensional systems theory","author":"NK Bose","year":"1982","unstructured":"Bose, N. K. (1982). Applied multidimensional systems theory. New York: Van Nostrand Reinhold."},{"key":"619_CR6","unstructured":"Boudellioua, M.\u00a0S. (2005). Equivalence to Smith form over a multivariate polynomial ring. In The fourth internatinal workshop on multidimensional systems (pp. 259\u2013262)."},{"key":"619_CR7","doi-asserted-by":"publisher","unstructured":"Boudellioua, M.\u00a0S., Galkowski, K., & Rogers, E. (2017). Equivalent 2-D nonsingular Roesser models for discrete linear repetitive processes. International Journal of Control, 1\u20139. \n                    https:\/\/doi.org\/10.1080\/00207179.2017.1414307","DOI":"10.1080\/00207179.2017.1414307"},{"key":"619_CR8","volume-title":"Linear system theory and design","author":"C Chen","year":"1995","unstructured":"Chen, C. (1995). Linear system theory and design. Oxford: Oxford University Press, Inc."},{"key":"619_CR9","unstructured":"Cockburn, J.\u00a0C. (2000). Multidimensional realizations of systems with parametric uncertainty. In Proceedings of MTNS (p.\u00a06)."},{"key":"619_CR10","unstructured":"Cunha, D.\u00a0P. (2013). Reduced order state-space models for 2-D systems. Master\u2019s thesis, Dept. Elect. Comput. Eng., Univ. Porto, Portugal."},{"key":"619_CR11","doi-asserted-by":"crossref","first-page":"115","DOI":"10.1016\/j.sysconle.2015.04.005","volume":"82","author":"D-W Ding","year":"2015","unstructured":"Ding, D.-W., Wang, H., & Li, X. (2015). $${H}_{-}\/{H}_{\\infty }$$ fault detection observer design for two-dimensional roesser systems. Systems & Control Letters, 82, 115\u2013120.","journal-title":"Systems & Control Letters"},{"key":"619_CR12","volume-title":"Modern control systems","author":"R\u00a0C Dorf","year":"2011","unstructured":"Dorf, R\u00a0. C., & Bishop, R\u00a0. H. (2011). Modern control systems. London: Pearson."},{"issue":"2","key":"619_CR13","doi-asserted-by":"crossref","first-page":"205","DOI":"10.1016\/S0005-1098(00)00155-2","volume":"37","author":"C Du","year":"2001","unstructured":"Du, C., Xie, L., & Zhang, C. (2001). $${H}_\\infty $$ control and robust stabilization of two-dimensional systems in Roesser models. Automatica, 37(2), 205\u2013211.","journal-title":"Automatica"},{"issue":"4","key":"619_CR14","doi-asserted-by":"crossref","first-page":"1727","DOI":"10.1007\/s11045-017-0523-7","volume":"29","author":"Z Feng","year":"2018","unstructured":"Feng, Z., & Xu, L. (2018). Optimization of coordinate transformation matrix for $${H}_\\infty $$ static-output-feedback control of 2-D discrete systems in FM second model. Multidimensional Systems and Signal Processing, 29(4), 1727\u20131737.","journal-title":"Multidimensional Systems and Signal Processing"},{"issue":"3","key":"619_CR15","doi-asserted-by":"crossref","first-page":"381","DOI":"10.1007\/s11045-011-0148-1","volume":"23","author":"Z-Y Feng","year":"2012","unstructured":"Feng, Z.-Y., Wu, Q., & Xu, L. (2012). $${H}_{\\infty }$$ control of linear multidimensional discrete systems. Multidimensional Systems and Signal Processing, 23(3), 381\u2013411.","journal-title":"Multidimensional Systems and Signal Processing"},{"issue":"4","key":"619_CR16","doi-asserted-by":"crossref","first-page":"484","DOI":"10.1109\/TAC.1976.1101305","volume":"21","author":"E Fornasini","year":"1976","unstructured":"Fornasini, E., & Marchesini, G. (1976). State space realization theory of two-dimensional filters. IEEE Transactions on Automatic Control, 21(4), 484\u2013492.","journal-title":"IEEE Transactions on Automatic Control"},{"key":"619_CR17","volume-title":"Control systems design: An introduction to state-space methods","author":"B Friedland","year":"1986","unstructured":"Friedland, B. (1986). Control systems design: An introduction to state-space methods. New York: McGraw-Hill."},{"key":"619_CR18","unstructured":"Galkowski, K. (2001). State space realization of linear 2-D systems with extensions to the general nD ($$n>2$$) case. London: Springer."},{"key":"619_CR19","volume-title":"Two-dimensional linear systems","author":"T Kaczorek","year":"1985","unstructured":"Kaczorek, T. (1985). Two-dimensional linear systems. London: Springer."},{"key":"619_CR20","unstructured":"Kaczorek, T. (1988). Singular models of 2-D systems. In Proceedings of the 12th World Congress on Scientific Computation, Paris (France)."},{"key":"619_CR21","volume-title":"Linear systems","author":"T Kailath","year":"1980","unstructured":"Kailath, T. (1980). Linear systems. Upper Saddle River: Prentice-Hall."},{"issue":"2","key":"619_CR22","doi-asserted-by":"crossref","first-page":"244","DOI":"10.1109\/31.20201","volume":"36","author":"Z Lin","year":"1989","unstructured":"Lin, Z., & Bruton, L. (1989). BIBO stability of inverse 2-D digital filters in the presence of nonessential singularities of the second kind. IEEE Transactions on Circuits and Systems, 36(2), 244\u2013254.","journal-title":"IEEE Transactions on Circuits and Systems"},{"issue":"3\u20134","key":"619_CR23","doi-asserted-by":"crossref","first-page":"329","DOI":"10.1023\/A:1011909707499","volume":"12","author":"Z Lin","year":"2001","unstructured":"Lin, Z., Lam, J., Galkowski, K., & Xu, S. (2001). A constructive approach to stabilizability and stabilization of a class of nD systems. Multidimensional Systems and Signal Processing, 12(3\u20134), 329\u2013343.","journal-title":"Multidimensional Systems and Signal Processing"},{"issue":"3","key":"619_CR24","doi-asserted-by":"crossref","first-page":"502","DOI":"10.1109\/9.376069","volume":"40","author":"W-S Lu","year":"1995","unstructured":"Lu, W.-S. (1995). On robust stability of 2-D discrete systems. IEEE Transactions on Automatic Control, 40(3), 502\u2013506.","journal-title":"IEEE Transactions on Automatic Control"},{"key":"619_CR25","unstructured":"Magni, J.-F. (2006). User manual of the linear fractional representation toolbox version 2.0. Systems Control and Flight Dynamics Department. \n                    http:\/\/w3.onera.fr\/smac\/lfrt\n                    \n                  . Accessed 17 Mar 2014."},{"key":"619_CR26","doi-asserted-by":"crossref","first-page":"22","DOI":"10.1016\/j.sysconle.2014.12.009","volume":"77","author":"W Paszke","year":"2015","unstructured":"Paszke, W., Dabkowski, P., Rogers, E., & Ga\u0142kowski, K. (2015). New results on strong practical stability and stabilization of discrete linear repetitive processes. Systems & Control Letters, 77, 22\u201329.","journal-title":"Systems & Control Letters"},{"issue":"1","key":"619_CR27","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1109\/TAC.1975.1100844","volume":"20","author":"R Roesser","year":"1975","unstructured":"Roesser, R. (1975). A discrete state-space model for linear image processing. IEEE Transactions on Automatic Control, 20(1), 1\u201310.","journal-title":"IEEE Transactions on Automatic Control"},{"key":"619_CR28","volume-title":"Control Systems theory and applications for linear repetitive processes. Control and information sciences","author":"E Rogers","year":"2007","unstructured":"Rogers, E., Galkowski, K., & Owens, D. H. (2007). Control Systems theory and applications for linear repetitive processes. Control and information sciences. Berlin, Heidelberg: Springer."},{"key":"619_CR29","unstructured":"Sulikowski, B. (2018). Robust $${H}_2$$ control of ladder circuits modeled as a subclass of $$2$$D systems. In Proceedings of the 17th annual European control conference (ECC2018) (pp. 888\u2013893). Limassol, Cyprus."},{"issue":"1","key":"619_CR30","doi-asserted-by":"crossref","first-page":"267","DOI":"10.1007\/s11045-013-0256-1","volume":"26","author":"B Sulikowski","year":"2015","unstructured":"Sulikowski, B., Galkowski, K., & Kummert, A. (2015). Proportional plus integral control of ladder circuits modeled in the form of two-dimensional (2D) systems. Multidimesional Systems and Signal Processing, 26(1), 267\u2013290.","journal-title":"Multidimesional Systems and Signal Processing"},{"issue":"11","key":"619_CR31","doi-asserted-by":"crossref","first-page":"1467","DOI":"10.1002\/cta.2328","volume":"45","author":"K Wang","year":"2017","unstructured":"Wang, K., Chen, M. Z., & Chen, G. (2017). Realization of a transfer function as a passive two-port RC ladder network with a specified gain. International Journal of Circuit Theory and Applications, 45(11), 1467\u20131481.","journal-title":"International Journal of Circuit Theory and Applications"},{"issue":"4","key":"619_CR32","doi-asserted-by":"crossref","first-page":"343","DOI":"10.1007\/s11045-010-0114-3","volume":"21","author":"L Xu","year":"2010","unstructured":"Xu, L., & Yan, S. (2010). A new elementary operation approach to multidimensional realization and LFR uncertainty modeling: The SISO case. Multidimensional Systems and Signal Processing, 21(4), 343\u2013372.","journal-title":"Multidimensional Systems and Signal Processing"},{"issue":"3","key":"619_CR33","doi-asserted-by":"crossref","first-page":"638","DOI":"10.1109\/TCSI.2011.2167262","volume":"59","author":"L Xu","year":"2012","unstructured":"Xu, L., Yan, S., Lin, Z., & Matsushita, S. (2012). A new elementary operation approach to multidimensional realization and LFR uncertainty modeling: The MIMO case. IEEE Transactions on Circuits and Systems-I, 59(3), 638\u2013651.","journal-title":"IEEE Transactions on Circuits and Systems-I"},{"key":"619_CR34","unstructured":"Yan, S., Xu, L., Zhang, Y., Cai, Y., & Zhao, D. (2018). Order evaluation to new elementary operation approach for MIMO multidimensional systems. International Journal of Control, (just-accepted):1\u201320."},{"issue":"3","key":"619_CR35","doi-asserted-by":"crossref","first-page":"789","DOI":"10.1109\/TCSI.2013.2283996","volume":"61","author":"S Yan","year":"2014","unstructured":"Yan, S., Xu, L., Zhao, Q., & Tian, Y. (2014). Elementary operation approach to order reduction for Roesser state-space model of multidimensional systems. IEEE Transactions on Circuits and Systems I: Regular Papers, 61(3), 789\u2013802.","journal-title":"IEEE Transactions on Circuits and Systems I: Regular Papers"},{"issue":"4","key":"619_CR36","doi-asserted-by":"crossref","first-page":"1417","DOI":"10.1007\/s11045-016-0418-z","volume":"28","author":"S Yan","year":"2017","unstructured":"Yan, S., Zhao, D., Xu, L., Cai, Y., & Li, Q. (2017). A novel elementary operation approach with Jordan transformation to order reduction for Roesser state-space model. Multidimensional Systems and Signal Processing, 28(4), 1417\u20131442.","journal-title":"Multidimensional Systems and Signal Processing"},{"issue":"3","key":"619_CR37","doi-asserted-by":"crossref","first-page":"410","DOI":"10.1109\/81.751317","volume":"46","author":"E Zerz","year":"1999","unstructured":"Zerz, E. (1999). LFT representations of parametrized polynomial systems. IEEE Transactions on Circuits and Systems I: Fundamental Theory and Applications, 46(3), 410\u2013416.","journal-title":"IEEE Transactions on Circuits and Systems I: Fundamental Theory and Applications"},{"key":"619_CR38","volume-title":"Topics in multidimensional linear systems theory","author":"E Zerz","year":"2000","unstructured":"Zerz, E. (2000). Topics in multidimensional linear systems theory. London: Springer."},{"key":"619_CR39","doi-asserted-by":"crossref","unstructured":"Zhao, D., Yan, S., Matsushita, S., & Xu, L. (2017). Order reduction for Roesser state-space model based on a certain system of equations. In 2017 10th international workshop on multidimensional (nD) systems (nDS) (pp. 1\u20135).","DOI":"10.1109\/NDS.2017.8070629"},{"issue":"4","key":"619_CR40","doi-asserted-by":"crossref","first-page":"1905","DOI":"10.1007\/s11045-017-0536-2","volume":"29","author":"D Zhao","year":"2018","unstructured":"Zhao, D., Yan, S., & Xu, L. (2018). Eigenvalue trim approach to exact order reduction for Roesser state-space model of multidimensional systems. Multidimensional Systems and Signal Processing, 29(4), 1905\u20131934.","journal-title":"Multidimensional Systems and Signal Processing"},{"key":"619_CR41","volume-title":"Robust and optimal control","author":"K Zhou","year":"1996","unstructured":"Zhou, K., Doyle, J\u00a0. C., & Glover, K. (1996). Robust and optimal control (Vol. 40). New Jersey: Prentice hall."}],"container-title":["Multidimensional Systems and Signal Processing"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s11045-018-0619-8.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s11045-018-0619-8\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s11045-018-0619-8.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,5,17]],"date-time":"2020-05-17T13:00:49Z","timestamp":1589720449000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s11045-018-0619-8"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2018,10,12]]},"references-count":41,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2019,7]]}},"alternative-id":["619"],"URL":"https:\/\/doi.org\/10.1007\/s11045-018-0619-8","relation":{},"ISSN":["0923-6082","1573-0824"],"issn-type":[{"value":"0923-6082","type":"print"},{"value":"1573-0824","type":"electronic"}],"subject":[],"published":{"date-parts":[[2018,10,12]]},"assertion":[{"value":"12 March 2018","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"20 July 2018","order":2,"name":"revised","label":"Revised","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"4 October 2018","order":3,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"12 October 2018","order":4,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}]}}