{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,28]],"date-time":"2025-10-28T14:58:08Z","timestamp":1761663488814,"version":"3.37.3"},"reference-count":53,"publisher":"Springer Science and Business Media LLC","issue":"4","license":[{"start":{"date-parts":[[2016,8,8]],"date-time":"2016-08-08T00:00:00Z","timestamp":1470614400000},"content-version":"unspecified","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"funder":[{"DOI":"10.13039\/100007458","name":"Qatar Foundation","doi-asserted-by":"publisher","award":["NPRP grant No. 4-195-2-065"],"award-info":[{"award-number":["NPRP grant No. 4-195-2-065"]}],"id":[{"id":"10.13039\/100007458","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":[[2017,10]]},"DOI":"10.1007\/s11045-016-0444-x","type":"journal-article","created":{"date-parts":[[2016,8,8]],"date-time":"2016-08-08T06:55:28Z","timestamp":1470639328000},"page":"1653-1678","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":5,"title":["A geometric approach to fault detection and isolation of multi-dimensional (n-D) systems"],"prefix":"10.1007","volume":"28","author":[{"given":"Amir","family":"Baniamerian","sequence":"first","affiliation":[]},{"given":"Nader","family":"Meskin","sequence":"additional","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0002-6919-3889","authenticated-orcid":false,"given":"Khashayar","family":"Khorasani","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2016,8,8]]},"reference":[{"key":"444_CR1","doi-asserted-by":"crossref","unstructured":"Baniamerian, A., & Khorasani, K. (2012). Fault detection and isolation of dissipative parabolic PDEs: Finite-dimensional geometric approach. In 2012 American control conference, pp. 5894\u20135899.","DOI":"10.1109\/ACC.2012.6315006"},{"key":"444_CR2","unstructured":"Baniamerian, A., Meskin, N., & Khorasani, K. (2013). Geometric fault detection and isolation of two-dimenional systems. In 2013 American control conference, pp. 3547\u20133554."},{"key":"444_CR3","doi-asserted-by":"crossref","unstructured":"Baniamerian, A., Meskin, N., & Khorasani, K. (2014a). Fault detection and isolation of Fornasini\u2013Marchesini 2D systems: A geometric approach. In 2014 American control conference, pp. 5527\u20135533.","DOI":"10.1109\/ACC.2014.6859030"},{"key":"444_CR4","doi-asserted-by":"crossref","unstructured":"Baniamerian, A., Meskin, N., & Khorasani, K. (2014b). Fault detection and isolation of Riesz spectral systems: A geometric approach. In 2014 European control conference, pp. 2145\u20132152.","DOI":"10.1109\/ECC.2014.6862357"},{"key":"444_CR5","volume-title":"Controlled and conditioned invariants in linear systems theory","author":"G Basile","year":"1992","unstructured":"Basile, G., & Marro, G. (1992). Controlled and conditioned invariants in linear systems theory. Englewood Cliffs: Prentice-Hall."},{"key":"444_CR6","doi-asserted-by":"crossref","first-page":"347","DOI":"10.1016\/0167-6911(85)90033-7","volume":"5","author":"M Bisiacco","year":"1985","unstructured":"Bisiacco, M. (1985). On the state reconstruction of 2D systems. Systems & Control Letters, 5, 347\u2013353.","journal-title":"Systems & Control Letters"},{"issue":"11","key":"444_CR7","doi-asserted-by":"crossref","first-page":"894","DOI":"10.1016\/j.sysconle.2006.05.003","volume":"55","author":"M Bisiacco","year":"2006","unstructured":"Bisiacco, M., & Valcher, M. E. (2006a). The general fault detection and isolation problem for 2D state-space models. Systems & Control Letters, 55(11), 894\u2013899.","journal-title":"Systems & Control Letters"},{"key":"444_CR8","doi-asserted-by":"crossref","first-page":"219","DOI":"10.1007\/s11045-005-6233-6","volume":"17","author":"M Bisiacco","year":"2006","unstructured":"Bisiacco, M., & Valcher, M. E. (2006b). Observer-based fault detection and isolation for 2D state-space models. Multidimensional Systems and Signal Processing, 17, 219\u2013242.","journal-title":"Multidimensional Systems and Signal Processing"},{"key":"444_CR9","doi-asserted-by":"crossref","first-page":"83","DOI":"10.1007\/s11045-010-0108-1","volume":"22","author":"B Cichy","year":"2011","unstructured":"Cichy, B., Galkowski, K., & Rogers, E. (2011). An approach to iterative learning control for spatio-temporal dynamics using n-D discrete linear systems models. Multidimensional Systems and Signal Processing, 22, 83\u201396.","journal-title":"Multidimensional Systems and Signal Processing"},{"key":"444_CR10","doi-asserted-by":"crossref","unstructured":"Conte, G., & Perdon, A. (1988). On the geometry of 2D systems. In IEEE international symposium on circuits and systems, pp. 97\u2013100.","DOI":"10.1109\/ISCAS.1988.14876"},{"issue":"5","key":"444_CR11","doi-asserted-by":"crossref","first-page":"1009","DOI":"10.1137\/0324059","volume":"24","author":"RF Curtain","year":"1986","unstructured":"Curtain, R. F. (1986). Invariance concepts in infinite dimensions. SIAM Journal on Control and Optimization, 24(5), 1009\u20131030.","journal-title":"SIAM Journal on Control and Optimization"},{"key":"444_CR12","doi-asserted-by":"crossref","unstructured":"Curtain, R. F., & Zwart, H. (1995). An introduction to infinite-dimensional linear systems theory, vol 21. Texts in Applied Mathematics. New York: Springer.","DOI":"10.1007\/978-1-4612-4224-6"},{"issue":"6","key":"444_CR13","doi-asserted-by":"crossref","first-page":"853","DOI":"10.1109\/9.928586","volume":"46","author":"C Persis De","year":"2001","unstructured":"De Persis, C., & Isidori, A. (2001). A geometric approach to nonlinear fault detection and isolation. Transactions on Automatic Control, 46(6), 853\u2013865.","journal-title":"Transactions on Automatic Control"},{"key":"444_CR14","doi-asserted-by":"crossref","first-page":"172","DOI":"10.1109\/TPAMI.1980.4766996","volume":"2","author":"E Fornasini","year":"1980","unstructured":"Fornasini, E., & Marchesini, G. (1980a). On the problems of constructing minimal realizations for two-dimensional filters. IEEE Transactions on Pattern Analysis and Machine Intelligence, 2, 172\u2013176.","journal-title":"IEEE Transactions on Pattern Analysis and Machine Intelligence"},{"issue":"12","key":"444_CR15","doi-asserted-by":"crossref","first-page":"1210","DOI":"10.1109\/TCS.1980.1084769","volume":"27","author":"E Fornasini","year":"1980","unstructured":"Fornasini, E., & Marchesini, G. (1980b). Stability analysis of 2-D systems. IEEE Transactions on Circuits and Systems, 27(12), 1210\u20131217.","journal-title":"IEEE Transactions on Circuits and Systems"},{"key":"444_CR16","doi-asserted-by":"crossref","unstructured":"Fornasini, E., & Marchesini, G. (1989). Residual generators for detecting failure in 2D systems. In Integrating Research, Industry and Education in Energy and Communication Engineering, MELECON\u201989, pp. 69\u201372.","DOI":"10.1109\/MELCON.1989.49983"},{"key":"444_CR17","first-page":"131","volume":"5","author":"E Fornasini","year":"1993","unstructured":"Fornasini, E., & Marchesini, G. (1993). Properties of pairs of matrices and state-models for two-dimensional systems. part1: State dynamics and geometry of the pairs. Multivariate Analysis: Future Directions, 5, 131\u2013180.","journal-title":"Multivariate Analysis: Future Directions"},{"issue":"4","key":"444_CR18","doi-asserted-by":"crossref","first-page":"387","DOI":"10.1023\/A:1008256224288","volume":"8","author":"E Fornasini","year":"1997","unstructured":"Fornasini, E., & Valcher, M. E. (1997). nD polynomial matrices with applications to multidimensional signal analysis. Multidimensional Systems and Signal Processing, 8(4), 387\u2013408.","journal-title":"Multidimensional Systems and Signal Processing"},{"issue":"4","key":"444_CR19","doi-asserted-by":"crossref","first-page":"421","DOI":"10.1002\/rnc.4590040403","volume":"4","author":"P Gahinet","year":"1994","unstructured":"Gahinet, P., & Apkarian, P. (1994). A linear matrix inequality approach to $${H}_\\infty $$ H \u221e control. International Journal of Robust and Nonlinear Control, 4(4), 421\u2013448.","journal-title":"International Journal of Robust and Nonlinear Control"},{"key":"444_CR20","doi-asserted-by":"crossref","DOI":"10.1007\/3-540-30368-5","volume-title":"Fault-diagnosis systems: An introduction from fault detection to fault tolerance","author":"R Isermann","year":"2006","unstructured":"Isermann, R. (2006). Fault-diagnosis systems: An introduction from fault detection to fault tolerance. Berlin: Springer."},{"issue":"9","key":"444_CR21","doi-asserted-by":"crossref","first-page":"1018","DOI":"10.1109\/PROC.1978.11079","volume":"66","author":"E Jury","year":"1978","unstructured":"Jury, E. (1978). Stability of multidimensional scalar and matrix polynomials. Proceedings of the IEEE, 66(9), 1018\u20131047.","journal-title":"Proceedings of the IEEE"},{"key":"444_CR22","volume-title":"Two-dimensional linear systems","author":"T Kaczorek","year":"1985","unstructured":"Kaczorek, T. (1985). Two-dimensional linear systems. Berlin: Springer."},{"issue":"5","key":"444_CR23","doi-asserted-by":"crossref","first-page":"671","DOI":"10.1109\/TAC.2005.846596","volume":"50","author":"T Kaczorek","year":"2005","unstructured":"Kaczorek, T. (2005). Generalization of cayley-hamilton theorem for n-D polynomial matrices. IEEE Transactions on Automatic Control, 50(5), 671\u2013674.","journal-title":"IEEE Transactions on Automatic Control"},{"issue":"10","key":"444_CR24","doi-asserted-by":"crossref","first-page":"2579","DOI":"10.1109\/TAC.2013.2264852","volume":"58","author":"S Knorn","year":"2013","unstructured":"Knorn, S., & Middleton, R. H. (2013). Stability of two-dimensional linear systems with singularities on the stability boundary using lmis. IEEE Transaction on Automatic Control, 58(10), 2579\u20132590.","journal-title":"IEEE Transaction on Automatic Control"},{"key":"444_CR25","unstructured":"Maleki, S., Rapisarda, P., Ntogramatzidis, L., & Rogers, E. (2013). A geometric approach to 3D fault identification. In Proceedings of the 8th international workshop on multidimensional systems, pp. 1\u20136."},{"issue":"2","key":"444_CR26","doi-asserted-by":"crossref","first-page":"481","DOI":"10.1007\/s11045-013-0271-2","volume":"26","author":"S Maleki","year":"2015","unstructured":"Maleki, S., Rapisarda, P., Ntogramatzidis, L., & Rogers, E. (2015). Failure identification for 3D linear systems. Multidimensional Systems and Signal Processing, 26(2), 481\u2013502.","journal-title":"Multidimensional Systems and Signal Processing"},{"key":"444_CR27","doi-asserted-by":"crossref","first-page":"11","DOI":"10.1016\/0307-904X(84)90170-7","volume":"8","author":"W Marszalek","year":"1984","unstructured":"Marszalek, W. (1984). Two-dimensional state-space discrete models for hyperbolic partial differential equations. Applied Mathematical Modeling, 8, 11\u201314.","journal-title":"Applied Mathematical Modeling"},{"key":"444_CR28","doi-asserted-by":"crossref","unstructured":"Massoumnia, M. A. (1986a). A geometric approach to failure detection and identification in linear systems. Ph.D. thesis, MIT, Dep. Aero. & Astro.","DOI":"10.21236\/ADA188277"},{"issue":"9","key":"444_CR29","doi-asserted-by":"crossref","first-page":"839","DOI":"10.1109\/TAC.1986.1104419","volume":"31","author":"MA Massoumnia","year":"1986","unstructured":"Massoumnia, M. A. (1986b). A geometric approach to the synthesis of failure detection filters. IEEE Transactions on Automatic Control, 31(9), 839\u2013846.","journal-title":"IEEE Transactions on Automatic Control"},{"issue":"3","key":"444_CR30","doi-asserted-by":"crossref","first-page":"316","DOI":"10.1109\/9.16422","volume":"34","author":"MA Massoumnia","year":"1989","unstructured":"Massoumnia, M. A., Verghese, G. C., & Willsky, A. (1989). Failure detection and identification. IEEE Transactions on Automatic Control, 34(3), 316\u2013321.","journal-title":"IEEE Transactions on Automatic Control"},{"issue":"11","key":"444_CR31","doi-asserted-by":"crossref","first-page":"2626","DOI":"10.1109\/TAC.2009.2031564","volume":"54","author":"D Meng","year":"2009","unstructured":"Meng, D., Jia, Y., Du, J., & Yuan, S. (2009). Robust discrete-time iterative learning control for nonlinear systems with varying initial state shifts. IEEE Transactions on Automatic Control, 54(11), 2626\u20132631.","journal-title":"IEEE Transactions on Automatic Control"},{"key":"444_CR32","doi-asserted-by":"crossref","first-page":"2032","DOI":"10.1016\/j.automatica.2009.04.020","volume":"45","author":"N Meskin","year":"2009","unstructured":"Meskin, N., & Khorasani, K. (2009a). Fault detection and isolation of discrete-time Markovian jump linear systems with application to a network of multi-agent systems having imperfect communication channels. Automatica, 45, 2032\u20132040.","journal-title":"Automatica"},{"key":"444_CR33","doi-asserted-by":"crossref","first-page":"2680","DOI":"10.1109\/TAC.2009.2031578","volume":"54","author":"N Meskin","year":"2009","unstructured":"Meskin, N., & Khorasani, K. (2009b). Fault detection and isolation of distributed time-delay systems. IEEE Trans Automatic Control, 54, 2680\u20132685.","journal-title":"IEEE Trans Automatic Control"},{"key":"444_CR34","doi-asserted-by":"crossref","first-page":"1567","DOI":"10.1016\/j.automatica.2009.02.019","volume":"45","author":"N Meskin","year":"2009","unstructured":"Meskin, N., & Khorasani, K. (2009c). Robust fault detection and isolation of time-delay systems using a geometric approach. Automatica, 45, 1567\u20131573.","journal-title":"Automatica"},{"issue":"6","key":"444_CR35","doi-asserted-by":"crossref","first-page":"1343","DOI":"10.1109\/TAC.2010.2042007","volume":"55","author":"N Meskin","year":"2010","unstructured":"Meskin, N., & Khorasani, K. (2010). A geometric approach to fault detection and isolation of continuous-time Markovian jump linear systems. IEEE Transactions on Automatic Control, 55(6), 1343\u20131357.","journal-title":"IEEE Transactions on Automatic Control"},{"issue":"8","key":"444_CR36","doi-asserted-by":"crossref","first-page":"1905","DOI":"10.1109\/TAC.2011.2129950","volume":"56","author":"N Meskin","year":"2011","unstructured":"Meskin, N., & Khorasani, K. (2011). Fault detection and isolation of linear impulsive systems. IEEE Transactions on Automatic Control, 56(8), 1905\u20131910.","journal-title":"IEEE Transactions on Automatic Control"},{"issue":"6","key":"444_CR37","first-page":"1422","volume":"18","author":"N Meskin","year":"2010","unstructured":"Meskin, N., Khorasani, K., & Rabbath, C. A. (2010a). A hybrid fault detection and isolation strategy for a network of unmanned vehicles in presence of large environmental disturbances. IEEE Transactions on Control Systems Technology, 18(6), 1422\u20131429.","journal-title":"IEEE Transactions on Control Systems Technology"},{"issue":"12","key":"444_CR38","doi-asserted-by":"crossref","first-page":"2879","DOI":"10.1049\/iet-cta.2009.0294","volume":"4","author":"N Meskin","year":"2010","unstructured":"Meskin, N., Khorasani, K., & Rabbath, C. A. (2010b). Hybrid fault detection and isolation strategy for non-linear systems in the presence of large environmental disturbances. IET Control Theory & Applications, 4(12), 2879\u20132895.","journal-title":"IET Control Theory & Applications"},{"issue":"1","key":"444_CR39","doi-asserted-by":"crossref","first-page":"334","DOI":"10.1137\/100815153","volume":"50","author":"L Ntogramatzidis","year":"2012","unstructured":"Ntogramatzidis, L. (2012). Structural invariants of two-dimensional systems. SIAM Journal on Control and Optimization, 50(1), 334\u2013356.","journal-title":"SIAM Journal on Control and Optimization"},{"key":"444_CR40","doi-asserted-by":"crossref","unstructured":"Ntogramatzidis, L., & Cantoni, M. (2012). Detectability subspaces and observer synthesis for two-dimensional systems. Multidimensional Systems and Signal Processing, pp. 1\u201318.","DOI":"10.1007\/s11045-010-0118-z"},{"issue":"8","key":"444_CR41","doi-asserted-by":"crossref","first-page":"1263","DOI":"10.1109\/81.873883","volume":"47","author":"T Ooba","year":"2000","unstructured":"Ooba, T. (2000). On stability analysis of 2-D systems based on 2-D Lyapunov matrix inequalities. IEEE Transactions on Circuits and Systems I: Fundamental Theory and Applications, 47(8), 1263\u20131265.","journal-title":"IEEE Transactions on Circuits and Systems I: Fundamental Theory and Applications"},{"issue":"7","key":"444_CR42","doi-asserted-by":"crossref","first-page":"1729","DOI":"10.1109\/TAC.2011.2135170","volume":"56","author":"GW Pulford","year":"2011","unstructured":"Pulford, G. W. (2011). The two-dimensional power spectral density: A connection between 2-D rational functions and linear systems. IEEE Transactions on Automatic Control, 56(7), 1729\u20131734.","journal-title":"IEEE Transactions on Automatic Control"},{"key":"444_CR43","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1109\/TAC.1975.1100844","volume":"20","author":"RP Roesser","year":"1975","unstructured":"Roesser, R. P. (1975). A discrete state-space model for linear image processing. IEEE Transaction on Automatic Control AC, 20, 1\u201310.","journal-title":"IEEE Transaction on Automatic Control AC"},{"issue":"1","key":"444_CR44","doi-asserted-by":"crossref","first-page":"7","DOI":"10.1023\/A:1008478411618","volume":"11","author":"E Rogers","year":"2000","unstructured":"Rogers, E., & Rocha, P. (2000). Guest editorial. Multidimensional Systems and Signal Processing, 11(1), 7\u20139.","journal-title":"Multidimensional Systems and Signal Processing"},{"issue":"2","key":"444_CR45","doi-asserted-by":"crossref","first-page":"181","DOI":"10.1109\/81.983866","volume":"49","author":"E Rogers","year":"2002","unstructured":"Rogers, E., Galkowski, K., Gramacki, A., Gramacki, J., & Owens, D. (2002). Stability and controllability of a class of 2-D linear systems with dynamic boundary conditions. IEEE Transactions on Circuits and Systems I: Fundamental Theory and Applications, 49(2), 181\u2013195.","journal-title":"IEEE Transactions on Circuits and Systems I: Fundamental Theory and Applications"},{"key":"444_CR46","unstructured":"Rogers, E., Galkowski, K., & Owens, D. H. (2007). Control systems theory and applications for linear repetitive processes, vol. 349. Lecture notes in control and information sciences, Berlin: Springer."},{"issue":"6","key":"444_CR47","doi-asserted-by":"crossref","first-page":"333","DOI":"10.1049\/ip-d.1983.0055","volume":"130","author":"P Stavroulakis","year":"1983","unstructured":"Stavroulakis, P., & Tzafestas, S. (1983). State reconstruction in low-sensitivity design of 3-dimensional systems. IEE Proceedings of Control Theory and Applications, Part D, 130(6), 333\u2013340.","journal-title":"IEE Proceedings of Control Theory and Applications, Part D"},{"key":"444_CR48","unstructured":"Vasilache, T., & Prepelita, V. (July, 2013). Observability and geometric approach of 2D hybrid systems. In The international conference on systems, control, signal processing and informatics, informatics, Greece, pp. 207\u2013214."},{"issue":"1","key":"444_CR49","doi-asserted-by":"crossref","first-page":"47","DOI":"10.1007\/s11045-013-0235-6","volume":"26","author":"R Wimalagunarathne","year":"2015","unstructured":"Wimalagunarathne, R., Wijenayake, C., Madanayake, A., Dansereau, D. G., & Bruton, L. T. (2015). Integral form 4-D light field filters using Xilinx FPGAs and 45 nm CMOS technology. Multidimensional Systems and Signal Processing, 26(1), 47\u201365.","journal-title":"Multidimensional Systems and Signal Processing"},{"key":"444_CR50","doi-asserted-by":"crossref","DOI":"10.1007\/978-1-4612-1082-5","volume-title":"Linear multivariable control: A geometric approach","author":"WM Wonham","year":"1985","unstructured":"Wonham, W. M. (1985). Linear multivariable control: A geometric approach (2nd ed.). Berlin: Springer.","edition":"2"},{"key":"444_CR51","doi-asserted-by":"crossref","unstructured":"Zerz, E., & Walcher, S. (2015). nD methods for 1D parameter-dependent systems. Multidimensional Systems and Signal Processing, pp. 1\u201312.","DOI":"10.1007\/s11045-015-0317-8"},{"issue":"5","key":"444_CR52","doi-asserted-by":"crossref","first-page":"351","DOI":"10.1007\/s00034-004-0804-x","volume":"23","author":"Y Zou","year":"2004","unstructured":"Zou, Y., Sheng, M., Zhong, N., & Xu, S. (2004). A generalized Kalman filter for 2D discrete systems. Circuits, Systems and Signal Processing, 23(5), 351\u2013364.","journal-title":"Circuits, Systems and Signal Processing"},{"key":"444_CR53","doi-asserted-by":"crossref","DOI":"10.1007\/BFb0044353","volume-title":"Geometric theory for infinite dimensional systems","author":"H Zwart","year":"1989","unstructured":"Zwart, H. (1989). Geometric theory for infinite dimensional systems (Vol. 115). Berlin: Springer."}],"container-title":["Multidimensional Systems and Signal Processing"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s11045-016-0444-x\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s11045-016-0444-x.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s11045-016-0444-x","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s11045-016-0444-x.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,9,12]],"date-time":"2019-09-12T04:26:34Z","timestamp":1568262394000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s11045-016-0444-x"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2016,8,8]]},"references-count":53,"journal-issue":{"issue":"4","published-print":{"date-parts":[[2017,10]]}},"alternative-id":["444"],"URL":"https:\/\/doi.org\/10.1007\/s11045-016-0444-x","relation":{},"ISSN":["0923-6082","1573-0824"],"issn-type":[{"type":"print","value":"0923-6082"},{"type":"electronic","value":"1573-0824"}],"subject":[],"published":{"date-parts":[[2016,8,8]]}}}