{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,11,10]],"date-time":"2025-11-10T13:37:04Z","timestamp":1762781824095,"version":"3.40.4"},"reference-count":103,"publisher":"Springer Science and Business Media LLC","issue":"2","license":[{"start":{"date-parts":[[2014,2,28]],"date-time":"2014-02-28T00:00:00Z","timestamp":1393545600000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Multidim Syst Sign Process"],"published-print":{"date-parts":[[2015,4]]},"DOI":"10.1007\/s11045-014-0280-9","type":"journal-article","created":{"date-parts":[[2014,2,27]],"date-time":"2014-02-27T19:36:36Z","timestamp":1393529796000},"page":"349-388","source":"Crossref","is-referenced-by-count":15,"title":["Recent progress in an algebraic analysis approach to linear systems"],"prefix":"10.1007","volume":"26","author":[{"given":"D.","family":"Robertz","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2014,2,28]]},"reference":[{"key":"280_CR1","unstructured":"Avanessoff, D., & Pomet, J.-B. (2007). Flatness and Monge parameterization of two-input systems, control-affine with 4 states or general with 3 states. ESAIM: Control, Optimisation and Calculus of Variations, 13(2), 237\u2013264 (electronic)."},{"key":"280_CR2","unstructured":"Barakat, M. (2001). Jets. A MAPLE-package for formal differential geometry. In V. G. Ganzha, E. W. Mayr, & E. V. Vorozhtsov (Eds.), Computer algebra in scientific computing CASC 2001 (pp. 1\u201312). Berlin: Springer."},{"key":"280_CR3","unstructured":"Barakat, M. (2010). Purity filtration and the fine structure of autonomy. In Proceedings of the 19th International Symposium on Mathematical Theory of Networks and Systems (MTNS 2010), Budapest, Hungary, 2010. Also in E. Zerz (Ed.) Algebraic Systems Theory, Behaviors, and Codes (pp. 1\u20136). Aachen: Shaker-Verlag."},{"issue":"3","key":"280_CR4","doi-asserted-by":"crossref","first-page":"299","DOI":"10.1142\/S0219498808002813","volume":"7","author":"M Barakat","year":"2008","unstructured":"Barakat, M., & Robertz, D. (2008). homalg: A meta-package for homological algebra. Journal of Algebra and its Applications, 7(3), 299\u2013317.","journal-title":"Journal of Algebra and its Applications"},{"key":"280_CR5","unstructured":"Bj\u00f6rk, J.-E. (1979). Rings of differential operators. Volume 21 of North-Holland Mathematical Library. Amsterdam: North-Holland Publishing Co."},{"key":"280_CR6","unstructured":"Blinkov, Y.A., Cid, C.F., Gerdt, V.P., Plesken, W., & Robertz, D. (2003) The MAPLE Package \u201cJanet\u201d: I. Polynomial Systems. II. Linear Partial Differential Equations. In V.G. Ganzha, E.W. Mayr, E.V. Vorozhtsov (eds.) Proceedings of the 6th International Workshop on Computer Algebra in Scientific Computing (pp. 31\u201340 resp. 41\u201354). Passau (Germany), 2003. http:\/\/wwwb.math.rwth-aachen.de\/Janet"},{"issue":"2\u20133","key":"280_CR7","doi-asserted-by":"crossref","first-page":"289","DOI":"10.1007\/s11786-010-0057-y","volume":"4","author":"MS Boudellioua","year":"2010","unstructured":"Boudellioua, M. S., & Quadrat, A. (2010). Serre\u2019s reduction of linear functional systems. Mathematics in Computer Science, 4(2\u20133), 289\u2013312.","journal-title":"Mathematics in Computer Science"},{"issue":"1","key":"280_CR8","doi-asserted-by":"crossref","first-page":"73","DOI":"10.1007\/s00200-009-0091-7","volume":"20","author":"F Boulier","year":"2009","unstructured":"Boulier, F., Lazard, D., Ollivier, F., & Petitot, M. (2009). Computing representations for radicals of finitely generated differential ideals. Applicable Algebra in Engineering, Communication and Computing, 20(1), 73\u2013121.","journal-title":"Applicable Algebra in Engineering, Communication and Computing"},{"key":"280_CR9","unstructured":"Bourbaki, N. (1980). Alg\u00e8bre, Chapter 10. Alg\u00e8bre homologique. Paris: Masson."},{"issue":"4","key":"280_CR10","doi-asserted-by":"crossref","first-page":"351","DOI":"10.1007\/s00498-012-0089-8","volume":"24","author":"H Bourl\u00e8s","year":"2012","unstructured":"Bourl\u00e8s, H., & Oberst, U. (2012). Elimination, fundamental principle and duality for analytic linear systems of partial differential-difference equations with constant coefficients. Mathematics of Control, Signals, and Systems, 24(4), 351\u2013402.","journal-title":"Mathematics of Control, Signals, and Systems"},{"key":"280_CR11","doi-asserted-by":"crossref","unstructured":"Buchberger, B. (2006). An algorithm for finding the basis elements of the residue class ring of a zero dimensional polynomial ideal. Journal of Symbolic Computations, 41(3\u20134), 475\u2013511. Translated from the 1965 German original by Michael P. Abramson.","DOI":"10.1016\/j.jsc.2005.09.007"},{"key":"280_CR12","first-page":"63","volume":"11","author":"N Caro","year":"2010","unstructured":"Caro, N., & Levcovitz, D. (2010). On a Theorem of Stafford. Cadernos de Mathem\u00e1tica, 11, 63\u201370.","journal-title":"Cadernos de Mathem\u00e1tica"},{"key":"280_CR13","unstructured":"Chakhar, A., Cluzeau, T., & Quadrat, A. (2011). An algebraic analysis approach to certain classes of nonlinear partial differential systems. In Proceedings of the 7th international workshop on multidimensional (nD) Systems. France: Poitiers."},{"key":"280_CR14","unstructured":"Chyzak, F. (1998). Fonctions holonomes en calcul formel. Palaiseau, France: Ph.D. thesis, Ecole Polytechnique."},{"issue":"5","key":"280_CR15","doi-asserted-by":"crossref","first-page":"319","DOI":"10.1007\/s00200-005-0188-6","volume":"16","author":"F Chyzak","year":"2005","unstructured":"Chyzak, F., Quadrat, A., & Robertz, D. (2005). Effective algorithms for parametrizing linear control systems over Ore algebras. Applicable Algebra in Engineering, Communication and Computing, 16(5), 319\u2013376.","journal-title":"Applicable Algebra in Engineering, Communication and Computing"},{"key":"280_CR16","doi-asserted-by":"crossref","unstructured":"Chyzak F., Quadrat A., & Robertz D., (2007). OreModules: a symbolic package for the study of multidimensional linear systems. In J. Chiasson, J.-J. Loiseau (Eds.) Applications of time delay systems. Volume 352 of Lecture Notes in Control and Information Sciences (pp. 233\u2013264). Berlin: Springer http:\/\/wwwb.math.rwth-aachen.de\/OreModules","DOI":"10.1007\/978-3-540-49556-7_15"},{"key":"280_CR17","doi-asserted-by":"crossref","first-page":"187","DOI":"10.1006\/jsco.1998.0207","volume":"26","author":"F Chyzak","year":"1998","unstructured":"Chyzak, F., & Salvy, B. (1998). Non-commutative elimination in Ore algebras proves multivariate identities. Journal of Symbolic Computation, 26, 187\u2013227.","journal-title":"Journal of Symbolic Computation"},{"issue":"1","key":"280_CR18","doi-asserted-by":"crossref","first-page":"324","DOI":"10.1016\/j.laa.2007.07.008","volume":"428","author":"T Cluzeau","year":"2008","unstructured":"Cluzeau, T., & Quadrat, A. (2008). Factoring and decomposing a class of linear functional systems. Linear Algebra and Its Applications, 428(1), 324\u2013381.","journal-title":"Linear Algebra and Its Applications"},{"key":"280_CR19","doi-asserted-by":"crossref","unstructured":"Cluzeau, T., & Quadrat, A. (2009). OreMorphisms: a homological algebraic package for factoring, reducing and decomposing linear functional systems. In J.-J. Loiseau, W. Michiels, S.-I. Niculescu, R. Sipahi (eds.), Topics in time delay systems. Volume 388 of Lecture Notes in Control and Information Sciences (pp. 179\u2013194). Springer, Berlin. Cf. also http:\/\/www-sop.inria.fr\/members\/Alban.Quadrat\/OreMorphisms or http:\/\/perso.ensil.unilim.fr\/cluzeau\/OreMorphisms","DOI":"10.1007\/978-3-642-02897-7_16"},{"issue":"10","key":"280_CR20","doi-asserted-by":"crossref","first-page":"1192","DOI":"10.1016\/j.jsc.2011.12.041","volume":"47","author":"T Cluzeau","year":"2012","unstructured":"Cluzeau, T., & Quadrat, A. (2012). Serre\u2019s reduction of linear partial differential systems with holonomic adjoints. Journal of Symbolic Computation, 47(10), 1192\u20131213.","journal-title":"Journal of Symbolic Computation"},{"key":"280_CR21","doi-asserted-by":"crossref","unstructured":"Cohn, P. M. (2006). Free ideal rings and localization in general rings. Volume 3 of New Mathematical Monographs. Cambridge: Cambridge University Press.","DOI":"10.1017\/CBO9780511542794"},{"key":"280_CR22","doi-asserted-by":"crossref","first-page":"417","DOI":"10.1112\/plms\/s3-57.3.417","volume":"57","author":"SC Coutinho","year":"1988","unstructured":"Coutinho, S. C., & Holland, M. P. (1988). Module structure of rings of differential operators. Proceedings of the London Mathematical Society, 57, 417\u2013432.","journal-title":"Proceedings of the London Mathematical Society"},{"key":"280_CR23","doi-asserted-by":"crossref","unstructured":"Diop, S. (1992). Differential-algebraic decision methods and some applications to system theory. Theoretical Computer Science, 98, 137\u2013161. Second Workshop on Algebraic and Computer-theoretic Aspects of Formal Power Series (Paris, 1990).","DOI":"10.1016\/0304-3975(92)90384-R"},{"key":"280_CR24","unstructured":"Ehrenpreis, L. (1970). Fourier analysis in several complex variables. Volume XVII of Pure and Applied Mathematics. New York-London-Sydney: Wiley-Interscience Publishers, Wiley."},{"key":"280_CR25","doi-asserted-by":"crossref","unstructured":"Eisenbud, D. (1995). Commutative algebra. Volume 150 of Graduate Texts in Mathematics. New York: Springer. With a view toward algebraic geometry.","DOI":"10.1007\/978-1-4612-5350-1"},{"key":"280_CR26","unstructured":"Fabia\u0144ska, A. (2009). Algorithmic analysis of presentations of groups and modules. Germany: Ph.D. thesis, RWTH Aachen University. This thesis is available at http:\/\/darwin.bth.rwth-aachen.de\/opus3\/volltexte\/2009\/2950 . QuillenSuslin project ( http:\/\/wwwb.math.rwth-aachen.de\/QuillenSuslin )"},{"key":"280_CR27","unstructured":"Fabia\u0144ska, A., & Quadrat, A. (2006). Flat multidimensional linear systems with constant coefficients are equivalent to controllable 1-D linear systems. In Proceedings of the 17th International Symposium on Mathematical Theory of Networks and Systems (MTNS 2006) (pp. 560\u2013582). Kyoto: Japan."},{"key":"280_CR28","unstructured":"Fabia\u0144ska, A., & Quadrat, A. (2007). Applications of the Quillen-Suslin theorem tomultidimensional systems theory. In H. Park & G. Regensburger (Eds.), Gr\u00f6bner bases in control theory and signal processing. Volume 3 of Radon Series on Computational and Applied Mathematics (pp. 23\u2013106). Berlin:Walter de Gruyter."},{"key":"280_CR29","doi-asserted-by":"crossref","first-page":"463","DOI":"10.1007\/978-3-662-08546-2_26","volume-title":"Mathematical system theory","author":"M Fliess","year":"1991","unstructured":"Fliess, M. (1991). Controllability revisited. In A. C. Antoulas (Ed.), Mathematical system theory (pp. 463\u2013474). Berlin: Springer. The influence of R. E. Kalman."},{"issue":"6","key":"280_CR30","doi-asserted-by":"crossref","first-page":"1327","DOI":"10.1080\/00207179508921959","volume":"61","author":"M Fliess","year":"1995","unstructured":"Fliess, M., L\u00e9vine, J., Martin, P., & Rouchon, P. (1995). Flatness and defect of non-linear systems: Introductory theory and examples. International Journal of Control, 61(6), 1327\u20131361.","journal-title":"International Journal of Control"},{"key":"280_CR31","doi-asserted-by":"crossref","first-page":"301","DOI":"10.1051\/cocv:1998111","volume":"3","author":"M Fliess","year":"1998","unstructured":"Fliess, M., & Mounier, H. (1998). Controllability and observability of linear delay systems: An algebraic approach. ESAIM: Control. Optimisation and Calculus of Variations, 3, 301\u2013314.","journal-title":"Optimisation and Calculus of Variations"},{"key":"280_CR32","doi-asserted-by":"crossref","unstructured":"Freund, E. (1971). Zeitvariable Mehrgr\u00f6\u00dfensysteme. Volume 57 of Lecture Notes in Operations Research and Mathematical Systems. Heidelberg: Springer.","DOI":"10.1007\/978-3-642-48185-7"},{"issue":"2","key":"280_CR33","doi-asserted-by":"crossref","first-page":"97","DOI":"10.1016\/S0167-6911(98)00041-3","volume":"35","author":"S Fr\u00f6hler","year":"1998","unstructured":"Fr\u00f6hler, S., & Oberst, U. (1998). Continuous time-varying linear systems. Systems & Control Letters, 35(2), 97\u2013110.","journal-title":"Systems & Control Letters"},{"issue":"6","key":"280_CR34","doi-asserted-by":"crossref","first-page":"845","DOI":"10.1016\/S0747-7171(03)00063-4","volume":"36","author":"J Gago-Vargas","year":"2003","unstructured":"Gago-Vargas, J. (2003). Bases for projective modules in $$A_n(k)$$ A n ( k ) . Journal of Symbolic Computation, 36(6), 845\u2013853.","journal-title":"Journal of Symbolic Computation"},{"issue":"1","key":"280_CR35","doi-asserted-by":"crossref","first-page":"50","DOI":"10.1080\/00927870903431209","volume":"39","author":"C Gallego","year":"2011","unstructured":"Gallego, C., & Lezama, O. (2011). Gr\u00f6bner bases for ideals of $$\\sigma \\text{- }PBW$$ \u03c3 - P B W extensions. Communications in Algebra, 39(1), 50\u201375.","journal-title":"Communications in Algebra"},{"key":"280_CR36","first-page":"199","volume-title":"Computational commutative and non-commutative algebraic geometry, NATO Science Series","author":"VP Gerdt","year":"2005","unstructured":"Gerdt, V. P. (2005). Involutive algorithms for computing Gr\u00f6bner bases. In S. Cojocaru, G. Pfister, & V. Ufnarovski (Eds.), Computational commutative and non-commutative algebraic geometry, NATO Science Series (pp. 199\u2013225). Amsterdam: IOS Press."},{"key":"280_CR37","doi-asserted-by":"crossref","unstructured":"Gluesing-Luerssen, H. (2002). Linear delay-differential systems with commensurate delays: An algebraic approach. Volume 1770 of Lecture Notes in Mathematics. Berlin: Springer.","DOI":"10.1007\/82934"},{"key":"280_CR38","first-page":"53","volume":"176","author":"DYu Grigor\u2019ev","year":"1989","unstructured":"Grigor\u2019ev, D Yu. (1989). Complexity of quantifier elimination in the theory of ordinary differentially closed fields. Zap. Nauchn. Sem. Leningrad. Otdel. Mat. Inst. Steklov. (LOMI), 176, 53\u201367.","journal-title":"Zap. Nauchn. Sem. Leningrad. Otdel. Mat. Inst. Steklov. (LOMI)"},{"issue":"3","key":"280_CR39","doi-asserted-by":"crossref","first-page":"456","DOI":"10.1016\/j.jpaa.2013.06.015","volume":"218","author":"L Guo","year":"2014","unstructured":"Guo, L., Regensburger, G., & Rosenkranz, M. (2014). On integro-differential algebras. Journal of Pure and Applied Algebra, 218(3), 456\u2013473.","journal-title":"Journal of Pure and Applied Algebra"},{"key":"280_CR40","doi-asserted-by":"crossref","first-page":"699","DOI":"10.1006\/jsco.2001.0491","volume":"32","author":"A Hillebrand","year":"2001","unstructured":"Hillebrand, A., & Schmale, W. (2001). Towards an effective version of a theorem of Stafford. Journal of Symbolic Computation, 32, 699\u2013716.","journal-title":"Journal of Symbolic Computation"},{"key":"280_CR41","unstructured":"Janet, M. (1929). Le\u00e7ons sur les syst\u00e8mes d\u2019\u00e9quations aux d\u00e9riv\u00e9es partielles. Cahiers Scientifiques, fasc. IV. Paris: Gauthiers-Villars."},{"key":"280_CR42","unstructured":"Janet, M. (1971). P. Zervos et le probl\u00e8me de Monge. Bull. Sci. Math. (2), 95, 15\u201326."},{"issue":"1","key":"280_CR43","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/S0747-7171(08)80003-X","volume":"9","author":"A Kandri-Rody","year":"1990","unstructured":"Kandri-Rody, A., & Weispfenning, V. (1990). Noncommutative Gr\u00f6bner bases in algebras of solvable type. Journal of Symbolic Computation, 9(1), 1\u201326.","journal-title":"Journal of Symbolic Computation"},{"key":"280_CR44","unstructured":"Kashiwara, M. (1995). Algebraic study of systems of partial differential equations, Volume 63. France (N.S.): M\u00e9m. Soc. Math."},{"key":"280_CR45","volume-title":"Solvable polynomial rings","author":"H Kredel","year":"1993","unstructured":"Kredel, H. (1993). Solvable polynomial rings. Aachen: Shaker."},{"key":"280_CR46","doi-asserted-by":"crossref","unstructured":"Lam, T. Y. (1999). Lectures on modules and rings. Volume 189 of Graduate Texts in Mathematics. New York: Springer.","DOI":"10.1007\/978-1-4612-0525-8"},{"key":"280_CR47","doi-asserted-by":"crossref","DOI":"10.1007\/978-3-540-34575-6","volume-title":"Serre\u2019s problem on projective modules. Springer Monographs in Mathematics","author":"TY Lam","year":"2006","unstructured":"Lam, T. Y. (2006). Serre\u2019s problem on projective modules. Springer Monographs in Mathematics. Berlin: Springer."},{"key":"280_CR48","unstructured":"Lange-Hegermann, M., & Robertz, D. (2013). Thomas decompositions of parametric nonlinear control systems. In Proceedings of the 5th Symposium on System Structure and Control (pp. 291\u2013296). France: Grenoble."},{"key":"280_CR49","unstructured":"Levandovskyy, V. (2005). Non-commutative computer algebra for polynomial algebras: Gr\u00f6bner bases, applications and implementation. Germany: Ph.D. thesis, University of Kaiserslautern. This thesis is available at http:\/\/kluedo.ub.uni-kl.de\/volltexte\/2005\/1883"},{"key":"280_CR50","unstructured":"Levandovskyy, V., & Zerz, E. (2005). Computer algebraic methods for the structural analysis of linear control systems. In Proceedings in Applied Mathematics and Mechanics (PAMM). Wiley-VCH. Cf. also http:\/\/www.math.rwth-aachen.de\/Eva.Zerz\/CLIPS\/"},{"issue":"1","key":"280_CR51","doi-asserted-by":"crossref","first-page":"47","DOI":"10.1007\/s00200-010-0137-x","volume":"22","author":"J L\u00e9vine","year":"2011","unstructured":"L\u00e9vine, J. (2011). On necessary and sufficient conditions for differential flatness. Applicable Algebra in Engineering, Communication and Computing, 22(1), 47\u201390.","journal-title":"Applicable Algebra in Engineering, Communication and Computing"},{"key":"280_CR52","doi-asserted-by":"crossref","first-page":"1535","DOI":"10.1016\/j.jsc.2004.07.003","volume":"38","author":"A Leykin","year":"2004","unstructured":"Leykin, A. (2004). Algorithmic proofs of two theorems of Stafford. Journal of Symbolic Computation, 38, 1535\u20131550.","journal-title":"Journal of Symbolic Computation"},{"key":"280_CR53","unstructured":"Leykin, A., & Tsai, H. Dmodules - Algorithms for $$D$$ D -modules. Macaulay2 package, http:\/\/www.math.uiuc.edu\/Macaulay2\/"},{"issue":"1","key":"280_CR54","doi-asserted-by":"crossref","first-page":"231","DOI":"10.1016\/0021-8693(92)90189-S","volume":"145","author":"A Logar","year":"1992","unstructured":"Logar, A., & Sturmfels, B. (1992). Algorithms for the Quillen-Suslin theorem. Journal of Algebra, 145(1), 231\u2013239.","journal-title":"Journal of Algebra"},{"issue":"6","key":"280_CR55","doi-asserted-by":"crossref","first-page":"707","DOI":"10.1016\/j.jsc.2005.01.004","volume":"30","author":"H Lombardi","year":"2005","unstructured":"Lombardi, H., & Yengui, I. (2005). Suslin\u2019s algorithms for reduction of unimodular rows. Journal of Symbolic Computation, 30(6), 707\u2013717.","journal-title":"Journal of Symbolic Computation"},{"key":"280_CR56","doi-asserted-by":"crossref","first-page":"175","DOI":"10.1023\/B:ACAP.0000013854.77539.53","volume":"80","author":"P Lu","year":"2004","unstructured":"Lu, P., Liu, M., & Oberst, U. (2004). Linear recurring arrays, linear systems and multidimensional cyclic codes over quasi-Frobenius rings. Acta Applicandae Mathematica, 80, 175\u2013198.","journal-title":"Acta Applicandae Mathematica"},{"key":"280_CR57","unstructured":"Malgrange, B. Syst\u00e8mes diff\u00e9rentiels \u00e0 coefficients constants. S\u00e9minaire Bourbaki, 246, 1962\u201364, 11 pages."},{"key":"280_CR58","unstructured":"McConnell, J. C., & Robson, J. C. (2000). Noncommutative Noetherian Rings. American Mathematical Society Providence, RI. With the cooperation of L. W. Small. Revision of the 1987 edition."},{"key":"280_CR59","unstructured":"Mounier, H. (1995). Propri\u00e9t\u00e9s structurelles des syst\u00e8mes lin\u00e9aires \u00e0 retards: Aspects th\u00e9oriques et pratiques. France: Ph.D. thesis, University of Orsay."},{"key":"280_CR60","unstructured":"Mounier, H., Rudolph, J., Petitot, M., & Fliess, M. (1995). A flexible rod as a linear delay system. In Proceedings of the 3rd European Control Conference Italy: Rome."},{"key":"280_CR61","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1007\/BF00046908","volume":"20","author":"U Oberst","year":"1990","unstructured":"Oberst, U. (1990). Multidimensional constant linear systems. Acta Applicandae Mathematica, 20, 1\u2013175.","journal-title":"Acta Applicandae Mathematica"},{"issue":"3","key":"280_CR62","doi-asserted-by":"crossref","first-page":"385","DOI":"10.1016\/S0098-1354(01)00752-9","volume":"26","author":"J Oldenburg","year":"2002","unstructured":"Oldenburg, J., & Marquardt, W. (2002). Flatness and higher order differential model representations in dynamic optimization. Computers & Chemical Engineering, 26(3), 385\u2013400.","journal-title":"Computers & Chemical Engineering"},{"key":"280_CR63","doi-asserted-by":"crossref","unstructured":"Palamodov, V. P. (1970). Linear differential operators with constant coefficients. Translated from the Russian by A. A. Brown. Volume 168 of Grundlehren der mathematischen Wissenschaften. New York: Springer.","DOI":"10.1007\/978-3-642-46219-1"},{"issue":"1","key":"280_CR64","doi-asserted-by":"crossref","first-page":"277","DOI":"10.1006\/jabr.1995.1349","volume":"178","author":"H Park","year":"1995","unstructured":"Park, H., & Woodburn, C. (1995). An algorithmic proof of Suslin\u2019s stability theorem for polynomial rings. Journal of Algebra, 178(1), 277\u2013298.","journal-title":"Journal of Algebra"},{"issue":"2","key":"280_CR65","doi-asserted-by":"crossref","first-page":"388","DOI":"10.1137\/S0363012997321784","volume":"37","author":"HK Pillai","year":"1998","unstructured":"Pillai, H. K., & Shankar, S. (1998). A behavioral approach to control of distributed systems. SIAM Journal on Control & Optimization, 37(2), 388\u2013408.","journal-title":"SIAM Journal on Control & Optimization"},{"key":"280_CR66","doi-asserted-by":"crossref","unstructured":"Polderman, J. W., & Willems, J. C. (1998). Introduction to mathematical systems theory. Volume 26 of Texts in applied mathematics. New York: Springer. A Behavioral Approach.","DOI":"10.1007\/978-1-4757-2953-5"},{"key":"280_CR67","unstructured":"Pommaret, J.-F. (1978). Systems of partial differential equations and Lie pseudogroups. Volume 14 of mathematics and its applications. New York: Gordon & Breach Science Publishers."},{"key":"280_CR68","unstructured":"Pommaret, J.-F. (1995). Dualit\u00e9 diff\u00e9rentielle et applications. Comptes rendus de l\u2019Acad\u00e9mie des sciences, Paris. S\u00e9rie 1. Math\u00e9matique, 320, 1225\u20131230."},{"key":"280_CR69","doi-asserted-by":"crossref","unstructured":"Pommaret, J.-F. (2001) Partial differential control theory. Volume 530 of Mathematics and its Applications. Dordrecht: Kluwer Academic Publishers Group. Vol. I. Mathematical tools; Vol. II. Control systems.","DOI":"10.1007\/978-94-010-0854-9_7"},{"issue":"3","key":"280_CR70","doi-asserted-by":"crossref","first-page":"275","DOI":"10.1093\/imamci\/16.3.275","volume":"16","author":"J-F Pommaret","year":"1999","unstructured":"Pommaret, J.-F., & Quadrat, A. (1999a). Algebraic analysis of linear multidimensional control systems. IMA Journal of Mathematical Control and Information, 16(3), 275\u2013297.","journal-title":"IMA Journal of Mathematical Control and Information"},{"issue":"4","key":"280_CR71","doi-asserted-by":"crossref","first-page":"247","DOI":"10.1016\/S0167-6911(99)00030-4","volume":"37","author":"J-F Pommaret","year":"1999","unstructured":"Pommaret, J.-F., & Quadrat, A. (1999b). Localization and parametrization of linear multidimensional control systems. Systems & Control Letters, 37(4), 247\u2013260.","journal-title":"Systems & Control Letters"},{"key":"280_CR72","unstructured":"Pommaret, J.-F., & Quadrat, A. (2000). Equivalences of linear control systems. In Proceedings of MTNS 2000. France: Perpignan."},{"key":"280_CR73","doi-asserted-by":"crossref","unstructured":"Pommaret, J.-F., & Quadrat A. (2003) A functorial approach to the behaviour of multidimensional control systems. International Journal of Applied Mathematics and Computer Science, 13(1), 7\u201313. Multidimensional systems $$n\\text{ D }$$ n D and iterative learning control (Czocha Castle, 2000).","DOI":"10.1007\/PL00009867"},{"key":"280_CR74","doi-asserted-by":"crossref","first-page":"821","DOI":"10.1080\/00207170410001726813","volume":"77","author":"J-F Pommaret","year":"2004","unstructured":"Pommaret, J.-F., & Quadrat, A. (2004). A differential operator approach to multidimensional optimal control. International Journal of Control, 77, 821\u2013836.","journal-title":"International Journal of Control"},{"key":"280_CR75","unstructured":"Quadrat, A. (1999). Analyse alg\u00e9brique des syst\u00e8mes de contr\u00f4le lin\u00e9aires multidimensionnels. France: Ph.D. thesis, Ecole Nationale des Ponts et Chauss\u00e9es."},{"key":"280_CR76","unstructured":"Quadrat, A. (2010a). Syst\u00e8mes et Structures: Une approche de la th\u00e9orie math\u00e9matique des syst\u00e8mes par l\u2019analyse alg\u00e9brique constructive. France: Habilitation thesis, Universit\u00e9 de Nice Sophia Antipolis."},{"key":"280_CR77","doi-asserted-by":"crossref","unstructured":"Quadrat, A. (2010b). An introduction to constructive algebraic analysis and its applications. In Les cours du CIRM, tome 1, num\u00e9ro 2: Journ\u00e9es Nationales de Calcul Formel (pp. 281\u2013471). Cf. also http:\/\/hal.archives-ouvertes.fr\/inria-00506104\/fr\/","DOI":"10.5802\/ccirm.11"},{"key":"280_CR78","doi-asserted-by":"crossref","first-page":"27","DOI":"10.1007\/s10440-012-9791-2","volume":"127","author":"A Quadrat","year":"2013","unstructured":"Quadrat, A. (2013). Grade filtration of linear functional systems. Acta Applicandae Mathematicae, 127, 27\u201386.","journal-title":"Acta Applicandae Mathematicae"},{"key":"280_CR79","unstructured":"Quadrat, A., & Regensburger, G. (2013). Polynomial solutions and annihilators of ordinary integro-differential operators. In Proceedings of the 5th Symposium on System Structure and Control (pp. 303\u2013308). France: Grenoble."},{"key":"280_CR80","doi-asserted-by":"crossref","unstructured":"Quadrat, A., & Robertz, D. (2005a). Parametrizing all solutions of uncontrollable multidimensional linear systems. In Proceedings of the 16th IFAC World Congress. Czech Republic: Prague.","DOI":"10.3182\/20050703-6-CZ-1902.00578"},{"key":"280_CR81","doi-asserted-by":"crossref","unstructured":"Quadrat, A., & Robertz, D. (2005b). On the blowing-up of stably free behaviours. In Proceedings of the 44th IEEE Conference on Decision and Control and European Control Conference ECC 2005 (pp. 1541\u20131546). Spain: Seville.","DOI":"10.1109\/CDC.2005.1582377"},{"key":"280_CR82","unstructured":"Quadrat, A., & Robertz, D. (2006a). Constructive computation of flat outputs of a class of multidimensional linear systems with variable coefficients. In Proceedings of the 17th International Symposium on Mathematical Theory of Networks and Systems (MTNS 2006) (pp. 583\u2013595). Kyoto: Japan."},{"key":"280_CR83","unstructured":"Quadrat, A., & Robertz, D. (2006b). On the Monge problem and multidimensional optimal control. In Proceedings of the 17th International Symposium on Mathematical Theory of Networks and Systems (MTNS 2006) (pp. 596\u2013605). Kyoto: Japan."},{"key":"280_CR84","doi-asserted-by":"crossref","unstructured":"Quadrat, A., & Robertz, D. (2007). Computation of bases of free modules over the Weyl algebras. Journal of Symbolic Computation, 42(11\u201312), 1113\u20131141. Stafford project ( http:\/\/wwwb.math.rwth-aachen.de\/OreModules )","DOI":"10.1016\/j.jsc.2007.06.005"},{"key":"280_CR85","unstructured":"Quadrat, A., & Robertz, D. (2008). Baer\u2019s extension problem for multidimensional linear systems. In Proceedings of the 18th international symposium on mathematical theory of networks and systems (MTNS 2008). USA: Virginia Tech, Blacksburg, Virginia."},{"key":"280_CR86","unstructured":"Quadrat, A., & Robertz, D. (2010). Controllability and differential flatness of linear analytic ordinary differential systems. In Proceedings of the 19th International Symposium on Mathematical Theory of Networks and Systems (MTNS 2010) Hungary: Budapest. Also in E. Zerz (eds.), Algebraic systems theory, behaviors, and codes (pp. 23\u201330). Shaker, Aachen."},{"key":"280_CR87","unstructured":"Quadrat, A., & Robertz, D. (2013). Stafford\u2019s reduction of linear partial differential systems. In Proceedings of the 5th Symposium on System Structure and Control (pp. 309\u2013314). Grenoble: France."},{"key":"280_CR88","unstructured":"Quadrat, A., & Robertz, D. (to appear). A constructive study of the module structure of rings of partial differential operators. Acta Applicandae Mathematicae."},{"key":"280_CR89","doi-asserted-by":"crossref","first-page":"167","DOI":"10.1007\/BF01390008","volume":"36","author":"D Quillen","year":"1976","unstructured":"Quillen, D. (1976). Projective modules over polynomial rings. Inventiones Mathematicae, 36, 167\u2013171.","journal-title":"Inventiones Mathematicae"},{"key":"280_CR90","unstructured":"Robertz, D. (2006). Formal computational methods for control theory. Ph.D. thesis, RWTH Aachen University, Germany. This thesis is available at http:\/\/darwin.bth.rwth-aachen.de\/opus\/volltexte\/2006\/1586"},{"key":"280_CR91","unstructured":"Robertz, D. (2007). Janet bases and applications. In M. Rosenkranz, D. Wang (Eds.) Gr\u00f3bner bases in symbolic analysis. Volume 2 of Radon Series on Computational and Applied Mathematics (pp.139\u2013168). Berlin: Walter de Gruyter."},{"key":"280_CR92","unstructured":"Robertz, D. (2012). Formal Algorithmic Elimination for PDEs. Habilitationsschrift, accepted by the Faculty of Mathematics, Computer Science and Natural Sciences, RWTH Aachen University. Submitted for publication."},{"key":"280_CR93","doi-asserted-by":"crossref","DOI":"10.1007\/b98977","volume-title":"An introduction to homological algebra","author":"JJ Rotman","year":"2009","unstructured":"Rotman, J. J. (2009). An introduction to homological algebra (2nd ed.). New York: Universitext. Springer.","edition":"2"},{"key":"280_CR94","unstructured":"Serre, J.-P. (1958) Modules projectifs et espaces fibr\u00e9s \u00e0 fibre vectorielle. In S\u00e9minaire P. Dubreil, M.-L. (Eds.) Dubreil-Jacotin et C. Pisot, 1957\/58, Fasc. 2, Expos\u00e9 23, Secr\u00e9tariat math\u00e9matique (pp. 1\u201318)."},{"key":"280_CR95","doi-asserted-by":"crossref","first-page":"429","DOI":"10.1112\/jlms\/s2-18.3.429","volume":"18","author":"JT Stafford","year":"1978","unstructured":"Stafford, J. T. (1978). Module structure of Weyl algebras. Journal of the London Mathematical Society, 18, 429\u2013442.","journal-title":"Journal of the London Mathematical Society"},{"key":"280_CR96","unstructured":"Suslin, A. A. (1976). Projective modules over a polynomial ring are free. Dokl. Akad. Nauk. S.S.S.R., 229, 1063\u20131066."},{"key":"280_CR97","volume-title":"Elimination methods. Texts and monographs in symbolic computation","author":"D Wang","year":"2001","unstructured":"Wang, D. (2001). Elimination methods. Texts and monographs in symbolic computation. Vienna: Springer."},{"issue":"1\u20132","key":"280_CR98","doi-asserted-by":"crossref","first-page":"11","DOI":"10.1023\/A:1008430528456","volume":"11","author":"J Wood","year":"2000","unstructured":"Wood, J. (2000). Modules and behaviours in $$n\\text{ D }$$ n D systems theory. Multidimensional Systems and Signal Processing, 11(1\u20132), 11\u201348.","journal-title":"Multidimensional Systems and Signal Processing"},{"key":"280_CR99","unstructured":"Zervos, P. (1932). Le probl\u00e8me de Monge. M\u00e9morial des Sciences Math\u00e9matiques, fasc. LIII. Gauthier-Villars."},{"key":"280_CR100","unstructured":"Zerz, E. (2000). Topics in multidimensional linear systems theory. Volume 256 of Lecture Notes in Control and Information Sciences. London: Springer."},{"key":"280_CR101","doi-asserted-by":"crossref","unstructured":"Zerz, E. (2001). Extension modules in behavioral linear systems theory. Multidimensional Systems and Signal Processing, 12(3\u20134), 309\u2013327. Special issue: Applications of Gr\u00f6bner bases to multidimensional systems and signal processing.","DOI":"10.1023\/A:1011905623429"},{"key":"280_CR102","doi-asserted-by":"crossref","first-page":"113","DOI":"10.1093\/imamci\/dni047","volume":"23","author":"E Zerz","year":"2006","unstructured":"Zerz, E. (2006). An algebraic analysis approach to linear time-varying systems. IMA Journal of Mathematical Control & Information, 23, 113\u2013126.","journal-title":"IMA Journal of Mathematical Control & Information"},{"key":"280_CR103","doi-asserted-by":"crossref","first-page":"1072","DOI":"10.1137\/S0363012900374749","volume":"40","author":"E Zerz","year":"2001","unstructured":"Zerz, E., & Lomadze, V. (2001). A constructive solution to interconnection and decomposition problems with multidimensional behaviors. SIAM Journal on Control & Optimization, 40, 1072\u20131086.","journal-title":"SIAM Journal on Control & Optimization"}],"container-title":["Multidimensional Systems and Signal Processing"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s11045-014-0280-9.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s11045-014-0280-9\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s11045-014-0280-9","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,5,1]],"date-time":"2025-05-01T23:21:49Z","timestamp":1746141709000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s11045-014-0280-9"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2014,2,28]]},"references-count":103,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2015,4]]}},"alternative-id":["280"],"URL":"https:\/\/doi.org\/10.1007\/s11045-014-0280-9","relation":{},"ISSN":["0923-6082","1573-0824"],"issn-type":[{"type":"print","value":"0923-6082"},{"type":"electronic","value":"1573-0824"}],"subject":[],"published":{"date-parts":[[2014,2,28]]}}}