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Volumn 351-352, Issue , 2002, Pages 761-798

Key problems in the extension of module-behaviour duality

Author keywords

Behaviors; Elimination problem; Image representations; Linear systems; Module theory; Multidimensional systems; Willems closure

Indexed keywords

ALGEBRA; LINEAR SYSTEMS;

EID: 31244432899     PISSN: 00243795     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0024-3795(01)00532-8     Document Type: Article
Times cited : (16)

References (45)
  • 1
    • 0031276796 scopus 로고    scopus 로고
    • Finite poles and zeros of linear systems: An intrinsic approach
    • H. Bourlès, and M. Fliess Finite poles and zeros of linear systems: an intrinsic approach Internat. J. Control 68 4 1997 897 922
    • (1997) Internat. J. Control , vol.68 , Issue.4 , pp. 897-922
    • Bourlès, H.1    Fliess, M.2
  • 2
    • 0003956966 scopus 로고
    • second ed. Wiley Chichester, UK
    • P.M. Cohn second ed. Algebra vol. 2 1989 Wiley Chichester, UK
    • (1989) Algebra , vol.2
    • Cohn, P.M.1
  • 4
    • 0003243860 scopus 로고
    • Commutative Algebra with a View Toward Algebraic Geometry
    • Springer Berlin
    • D. Eisenbud Commutative Algebra with a View Toward Algebraic Geometry Graduate Texts in Mathematics vol. 150 1995 Springer Berlin
    • (1995) Graduate Texts in Mathematics , vol.150
    • Eisenbud, D.1
  • 5
    • 0002103461 scopus 로고
    • Direct methods for primary decomposition
    • D. Eisenbud, C. Huneke, and W. Vasconcelos Direct methods for primary decomposition Invent. Math. 110 2 1992 207 235
    • (1992) Invent. Math. , vol.110 , Issue.2 , pp. 207-235
    • Eisenbud, D.1    Huneke, C.2    Vasconcelos, W.3
  • 6
    • 0025643607 scopus 로고
    • Some basic structural properties of generalized linear systems
    • M. Fliess Some basic structural properties of generalized linear systems Systems Control Lett. 15 1990 391 396
    • (1990) Systems Control Lett. , vol.15 , pp. 391-396
    • Fliess, M.1
  • 8
    • 0026898413 scopus 로고
    • A remark on Willems' trajectory characterization of linear controllability
    • M. Fliess A remark on Willems' trajectory characterization of linear controllability Systems Control Lett. 19 1992 43 45
    • (1992) Systems Control Lett. , vol.19 , pp. 43-45
    • Fliess, M.1
  • 9
    • 0029327262 scopus 로고
    • Flatness and defect of non-linear systems: Introductory theory and examples
    • M. Fliess, J. Lévine, P. Martin, and P. Rouchon Flatness and defect of non-linear systems: introductory theory and examples Internat. J. Control 61 6 1995 1327 1361
    • (1995) Internat. J. Control , vol.61 , Issue.6 , pp. 1327-1361
    • Fliess, M.1    Lévine, J.2    Martin, P.3    Rouchon, P.4
  • 10
    • 0032156647 scopus 로고    scopus 로고
    • Continuous time-varying linear systems
    • S. Fröhler, and U. Oberst Continuous time-varying linear systems Systems Control Lett. 35 2 1998 97 110
    • (1998) Systems Control Lett. , vol.35 , Issue.2 , pp. 97-110
    • Fröhler, S.1    Oberst, U.2
  • 11
    • 0001832313 scopus 로고    scopus 로고
    • Completion of linear differential systems to involution
    • V.G. Ganzha, E.W. Mayr, E.V. Vorozhtsov, Springer Berlin
    • V. Gerdt Completion of linear differential systems to involution V.G. Ganzha, E.W. Mayr, E.V. Vorozhtsov, Computer Algebra in Scientific Computing 1999 Springer Berlin 115 137
    • (1999) Computer Algebra in Scientific Computing , pp. 115-137
    • Gerdt, V.1
  • 12
    • 85025504292 scopus 로고
    • Gröbner basis and primary decomposition of polynomial ideals
    • P. Gianni, B. Trager, and G. Zacharias Gröbner basis and primary decomposition of polynomial ideals J. Symbolic Comput. 6 1988 149 167
    • (1988) J. Symbolic Comput. , vol.6 , pp. 149-167
    • Gianni, P.1    Trager, B.2    Zacharias, G.3
  • 13
    • 0031102346 scopus 로고    scopus 로고
    • A behavioral approach to delay-differential systems
    • H. Glüsing-Lürßen A behavioral approach to delay-differential systems SIAM J. Control Optim. 35 2 1997 480 499
    • (1997) SIAM J. Control Optim. , vol.35 , Issue.2 , pp. 480-499
    • Glüsing-Lürßen, H.1
  • 15
    • 0033336988 scopus 로고    scopus 로고
    • System equivalence for AR-systems over rings - With an application to delay-differential systems
    • L.C.G.J.M. Habets System equivalence for AR-systems over rings - with an application to delay-differential systems Math. Control Signals Systems 12 1999 219 244
    • (1999) Math. Control Signals Systems , vol.12 , pp. 219-244
    • Habets, L.C.G.J.M.1
  • 16
    • 0002856938 scopus 로고
    • Les systèms d'équations aux dérivées partielles
    • M. Janet Les systèms d'équations aux dérivées partielles J. Math. Pure Appl. 3 1920 65
    • (1920) J. Math. Pure Appl. , vol.3 , pp. 65
    • Janet, M.1
  • 17
    • 0008762241 scopus 로고
    • Closed subspaces, polynomial operators in the shift, and ARMA representations
    • J. Komorník, P. Rocha, and J.C. Willems Closed subspaces, polynomial operators in the shift, and ARMA representations Appl. Math. Lett. 4 3 1991 15 19
    • (1991) Appl. Math. Lett. , vol.4 , Issue.3 , pp. 15-19
    • Komorník, J.1    Rocha, P.2    Willems, J.C.3
  • 18
    • 0003363507 scopus 로고    scopus 로고
    • Lectures on Modules and Rings
    • Springer Berlin
    • T.Y. Lam Lectures on Modules and Rings Graduate Texts in Mathematics vol. 189 1999 Springer Berlin
    • (1999) Graduate Texts in Mathematics , vol.189
    • Lam, T.Y.1
  • 19
    • 0003232367 scopus 로고
    • Finite-dimensional time-invariant linear dynamical systems: Algebraic theory
    • V. Lomadze Finite-dimensional time-invariant linear dynamical systems: algebraic theory Acta Appl. Math. 19 1990 149 201
    • (1990) Acta Appl. Math. , vol.19 , pp. 149-201
    • Lomadze, V.1
  • 24
    • 0003034426 scopus 로고
    • Multidimensional constant linear systems
    • U. Oberst Multidimensional constant linear systems Acta Appl. Math. 20 1990 1 175
    • (1990) Acta Appl. Math. , vol.20 , pp. 1-175
    • Oberst, U.1
  • 25
    • 0000391502 scopus 로고
    • Variations on the fundamental principle for linear systems of partial differential and difference equations with constant coefficients
    • U. Oberst Variations on the fundamental principle for linear systems of partial differential and difference equations with constant coefficients Appl. Algebra Engrg. Comm. Comput. 6 4/5 1995 211 243
    • (1995) Appl. Algebra Engrg. Comm. Comput. , vol.6 , Issue.4-5 , pp. 211-243
    • Oberst, U.1
  • 27
    • 0032201987 scopus 로고    scopus 로고
    • A behavioral approach to control of distributed systems
    • H. Pillai, and S. Shankar A behavioral approach to control of distributed systems SIAM J. Control Optim. 37 2 1998 388 408
    • (1998) SIAM J. Control Optim. , vol.37 , Issue.2 , pp. 388-408
    • Pillai, H.1    Shankar, S.2
  • 29
    • 0033187892 scopus 로고    scopus 로고
    • Algebraic analysis of linear multidimensional control systems
    • J.-F. Pommaret, and A. Quadrat Algebraic analysis of linear multidimensional control systems IMA J. Math. Control Inform. 16 1999 275 297
    • (1999) IMA J. Math. Control Inform. , vol.16 , pp. 275-297
    • Pommaret, J.-F.1    Quadrat, A.2
  • 30
    • 0033671259 scopus 로고    scopus 로고
    • Formal elimination for multidimensional systems and applications to control theory
    • J.-F. Pommaret, and A. Quadrat Formal elimination for multidimensional systems and applications to control theory Math. Control Signals Systems 13 3 2000 193 215
    • (2000) Math. Control Signals Systems , vol.13 , Issue.3 , pp. 193-215
    • Pommaret, J.-F.1    Quadrat, A.2
  • 31
    • 84943791690 scopus 로고    scopus 로고
    • A functorial approach to the behaviour of multidimensional control systems
    • (to appear)
    • J.-F. Pommaret, and A. Quadrat A functorial approach to the behaviour of multidimensional control systems Appl. Math. Comput. Science 2001 (to appear)
    • (2001) Appl. Math. Comput. Science
    • Pommaret, J.-F.1    Quadrat, A.2
  • 35
    • 0033227788 scopus 로고    scopus 로고
    • The Nullstellensatz for systems of PDE
    • S. Shankar The Nullstellensatz for systems of PDE Adv. Appl. Math. 23 4 1999 360 374
    • (1999) Adv. Appl. Math. , vol.23 , Issue.4 , pp. 360-374
    • Shankar, S.1
  • 37
    • 0042975253 scopus 로고
    • Overdetermined systems of partial differential equations
    • D.C. Spencer Overdetermined systems of partial differential equations Bull. Am. Math. Soc. 75 1965 1 114
    • (1965) Bull. Am. Math. Soc. , vol.75 , pp. 1-114
    • Spencer, D.C.1
  • 39
    • 0026119885 scopus 로고
    • Paradigms and puzzles in the theory of dynamical systems
    • J.C. Willems Paradigms and puzzles in the theory of dynamical systems IEEE Trans. Auto. Control 36 3 1991 259 294
    • (1991) IEEE Trans. Auto. Control , vol.36 , Issue.3 , pp. 259-294
    • Willems, J.C.1
  • 40
    • 0031100338 scopus 로고    scopus 로고
    • On interconnections, control, and feedback
    • J.C. Willems On interconnections, control, and feedback IEEE Trans. Auto. Control 42 4 1997 458 472
    • (1997) IEEE Trans. Auto. Control , vol.42 , Issue.4 , pp. 458-472
    • Willems, J.C.1
  • 41
    • 0033717468 scopus 로고    scopus 로고
    • Modules and behaviours in nD systems theory
    • J. Wood Modules and behaviours in nD systems theory Multidimensional Systems Signal Process. 11 1-2 2000 11 48
    • (2000) Multidimensional Systems Signal Process. , vol.11 , Issue.1-2 , pp. 11-48
    • Wood, J.1
  • 43
    • 0002570734 scopus 로고    scopus 로고
    • Notes on the definition of behavioural controllability
    • J. Wood, and E. Zerz Notes on the definition of behavioural controllability Systems Control Lett. 37 1999 31 37
    • (1999) Systems Control Lett. , vol.37 , pp. 31-37
    • Wood, J.1    Zerz, E.2
  • 44
    • 0030284047 scopus 로고    scopus 로고
    • Primeness of multivariate polynomial matrices
    • E. Zerz Primeness of multivariate polynomial matrices Systems Control Lett. 29 3 1996 139 146
    • (1996) Systems Control Lett. , vol.29 , Issue.3 , pp. 139-146
    • Zerz, E.1
  • 45
    • 0035385820 scopus 로고    scopus 로고
    • Extension modules in behavioral linear systems theory
    • (submitted to)
    • E. Zerz Extension modules in behavioral linear systems theory Multidimensional Systems Signal Process. 12 3-4 2001 309 327 (submitted to)
    • (2001) Multidimensional Systems Signal Process. , vol.12 , Issue.3-4 , pp. 309-327
    • Zerz, E.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.