메뉴 건너뛰기




Volumn 42, Issue 1, 2003, Pages 266-299

The fractional representation approach to synthesis problems: An algebraic analysis viewpoint part I: (weakly) doubly coprime factorizations

(1)  Quadrat, A a  

a INRIA   (France)

Author keywords

(weakly) left right doubly coprime factorizations; Algebraic analysis; B zout domains; Coherent rings and modules; Coherent Sylvester domains; Fractional representation approach to synthesis problems; H ( +)

Indexed keywords

GRAPH THEORY; INTEGRATION; MATRIX ALGEBRA; SYSTEM STABILITY; SYSTEMS ANALYSIS;

EID: 0043259791     PISSN: 03630129     EISSN: None     Source Type: Journal    
DOI: 10.1137/S0363012902417127     Document Type: Article
Times cited : (38)

References (52)
  • 2
    • 0004150533 scopus 로고
    • Masson, Paris, Chapter 10
    • N. BOURBAKI, Algèbre, Masson, Paris, 1980, Chapter 10.
    • (1980) Algèbre
    • Bourbaki, N.1
  • 3
    • 0002331968 scopus 로고
    • Stabilization, tracking and disturbance rejection in multi-variable convolution systems
    • F. M. CALLIER AND C. A. DESOER, Stabilization, tracking and disturbance rejection in multi-variable convolution systems, Ann. Soc. Sci. Bruxelles, 94 (1980), pp. 5-51.
    • (1980) Ann. Soc. Sci. Bruxelles , vol.94 , pp. 5-51
    • Callier, F.M.1    Desoer, C.A.2
  • 4
    • 0040743896 scopus 로고
    • Idéaux des fonctions analytiques de n variables complexes
    • H. CARTAN, Idéaux des fonctions analytiques de n variables complexes, Ann. Ecole Norm. Sup., 61 (1944), pp. 149-197.
    • (1944) Ann. Ecole Norm. Sup. , vol.61 , pp. 149-197
    • Cartan, H.1
  • 5
    • 84968484219 scopus 로고
    • Direct product of modules
    • S. U. CHASE, Direct product of modules, Trans. AMS, 97 (1960), pp. 457-473.
    • (1960) Trans. AMS , vol.97 , pp. 457-473
    • Chase, S.U.1
  • 7
    • 0019900095 scopus 로고
    • Systems over a principal ideal domain. A polynomial model approach
    • G. CONTE AND A. M. PERDON, Systems over a principal ideal domain. A polynomial model approach, SIAM. J. Control Optim., 20 (1982), pp. 112-124.
    • (1982) SIAM. J. Control Optim. , vol.20 , pp. 112-124
    • Conte, G.1    Perdon, A.M.2
  • 8
    • 0001773481 scopus 로고
    • An Introduction to Infinite-Dimensional Linear Systems Theory
    • Springer-Verlag, New York
    • R. F. CURTAIN AND H. J. ZWART, An Introduction to Infinite-Dimensional Linear Systems Theory, Texts Appl. Math. 21, Springer-Verlag, New York, 1991.
    • (1991) Texts Appl. Math. , vol.21
    • Curtain, R.F.1    Zwart, H.J.2
  • 9
    • 0019031668 scopus 로고
    • Feedback system design: The fractional representation approach to analysis and synthesis
    • C. A. DESOER, R. -W. LIU, J. MURRAY, AND R. SAEKS, Feedback system design: The fractional representation approach to analysis and synthesis, IEEE Trans. Automat. Control, 25 (1980), pp. 399-412.
    • (1980) IEEE Trans. Automat. Control , vol.25 , pp. 399-412
    • Desoer, C.A.1    Liu, R.-W.2    Murray, J.3    Saeks, R.4
  • 11
    • 0002369348 scopus 로고
    • Free algebras over Bézout domains are Sylvester domains
    • W. DICKS, Free algebras over Bézout domains are Sylvester domains, J. Pure Appl. Algebra, 27 (1983), pp. 15-28.
    • (1983) J. Pure Appl. Algebra , vol.27 , pp. 15-28
    • Dicks, W.1
  • 12
    • 1842474184 scopus 로고    scopus 로고
    • private communication, Universitat Autònoma de Barcelona, Barcelona, Spain
    • W. DICKS, private communication, Universitat Autònoma de Barcelona, Barcelona, Spain, 2001.
    • (2001)
    • Dicks, W.1
  • 13
    • 0003207876 scopus 로고
    • Commutative Algebra with a View Toward Algebraic Geometry
    • Springer-Verlag, New York
    • D. EISENBUD, Commutative Algebra with a View Toward Algebraic Geometry, Grad. Texts in Math. 150, Springer-Verlag, New York, 1994.
    • (1994) Grad. Texts in Math. , vol.150
    • Eisenbud, D.1
  • 14
    • 31844446903 scopus 로고
    • Coherent rings of finite weak global dimension
    • M. FINKEL JONES AND M. L. TELPY, Coherent rings of finite weak global dimension, Communications in Algebra, 10 (1982), pp. 493-503.
    • (1982) Communications in Algebra , vol.10 , pp. 493-503
    • Finkel Jones, M.1    Telpy, M.L.2
  • 15
    • 0003276994 scopus 로고    scopus 로고
    • Modules over Non-Noetherian Domains
    • American Mathematical Society, Providence, RI
    • L. FUCHS AND L. SALCE, Modules over Non-Noetherian Domains, Math. Surveys Monogr. 84, American Mathematical Society, Providence, RI, 2000.
    • (2000) Math. Surveys Monogr. , vol.84
    • Fuchs, L.1    Salce, L.2
  • 17
    • 1842526346 scopus 로고
    • Commutative coherent rings: Historical perspective and current developments
    • S. GLAZ, Commutative coherent rings: Historical perspective and current developments, Nieuw Arch. Wiskd., 10 (1992), pp. 27-56.
    • (1992) Nieuw Arch. Wiskd. , vol.10 , pp. 27-56
    • Glaz, S.1
  • 18
    • 84968474701 scopus 로고
    • Divisibility properties of integral functions
    • O. HELMER, Divisibility properties of integral functions, Duke Math. J., 6 (1940), pp. 345-356.
    • (1940) Duke Math. J. , vol.6 , pp. 345-356
    • Helmer, O.1
  • 20
    • 0003267890 scopus 로고
    • Serre's Conjecture
    • Springer-Verlag, New York
    • T. Y. LAM, Serre's Conjecture, Lecture Notes in Math., 635, Springer-Verlag, New York, 1978.
    • (1978) Lecture Notes in Math. , vol.635
    • Lam, T.Y.1
  • 21
    • 0033741764 scopus 로고    scopus 로고
    • Algebraic tools for the control and stabilization of time-delay systems
    • J. J. LOISEAU, Algebraic tools for the control and stabilization of time-delay systems, IFAC Reviews, Annual Reviews in Control, 24 (2000), pp. 135-149.
    • (2000) IFAC Reviews, Annual Reviews in Control , vol.24 , pp. 135-149
    • Loiseau, J.J.1
  • 22
    • 0035661807 scopus 로고    scopus 로고
    • Feedback stabilization over commutative rings: Further study of coordinate-free approach
    • K. MORI AND K. ABE, Feedback stabilization over commutative rings: Further study of coordinate-free approach, SIAM J. Control Optim., 39 (2001), pp. 1952-1973.
    • (2001) SIAM J. Control Optim. , vol.39 , pp. 1952-1973
    • Mori, K.1    Abe, K.2
  • 23
    • 0002394309 scopus 로고
    • Coherence of some rings of functions
    • W. S. MCVOY AND L. A. RUBEL, Coherence of some rings of functions, J. Funct. Anal., 21 (1976), pp. 76-87.
    • (1976) J. Funct. Anal. , vol.21 , pp. 76-87
    • McVoy, W.S.1    Rubel, L.A.2
  • 24
    • 1842526344 scopus 로고
    • Homological dimensions of finitely presented modules
    • D. G. MCRAE, Homological dimensions of finitely presented modules, Math. Scand., 28 (1971), pp. 70-76.
    • (1971) Math. Scand. , vol.28 , pp. 70-76
    • McRae, D.G.1
  • 26
    • 0003034426 scopus 로고
    • Multidimensional Constant Linear Systems
    • U. OBERST, Multidimensional Constant Linear Systems, Acta Appl. Math., 20 (1990), pp. 1-175.
    • (1990) Acta Appl. Math. , vol.20 , pp. 1-175
    • Oberst, U.1
  • 27
    • 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), pp. 275-297.
    • (1999) IMA J. Math. Control Inform. , vol.16 , pp. 275-297
    • Pommaret, J.F.1    Quadrat, A.2
  • 28
    • 84994453812 scopus 로고    scopus 로고
    • A functorial approach to the behaviour of multidimensional control systems
    • Czocha Castle, Poland; to appear in Applied Mathematics and Computer Science
    • J. F. POMMARET AND A. QUADRAT, A functorial approach to the behaviour of multidimensional control systems, in Proceedings of the 2nd International Workshop on Multidimensional Systems (NDS), Czocha Castle, Poland, 2000, pp. 91-96; to appear in Applied Mathematics and Computer Science.
    • (2000) Proceedings of the 2nd International Workshop on Multidimensional Systems (NDS) , pp. 91-96
    • Pommaret, J.F.1    Quadrat, A.2
  • 32
    • 1842421706 scopus 로고    scopus 로고
    • Une approche de la stabilisation par l'analyse algébrique, Partie I. Factorisations doublement faiblement copremières, Partie II. Stabilisation interne, Partie III. Sur une structure générale des contrôleurs stabilisants basée sur le rang stable
    • Nantes, France, CD-ROM
    • A. QUADRAT, Une approche de la stabilisation par l'analyse algébrique, Partie I. Factorisations doublement faiblement copremières, Partie II. Stabilisation interne, Partie III. Sur une structure générale des contrôleurs stabilisants basée sur le rang stable, in Proceedings of the Conférence Internationale Francophone d'Automatique (CIFA), Nantes, France, CD-ROM, 2002; available online at www.irccyn.ec-nantes.fr/cifa/.
    • (2002) Proceedings of the Conférence Internationale Francophone d'Automatique (CIFA)
    • Quadrat, A.1
  • 33
    • 0041756701 scopus 로고    scopus 로고
    • The fractional representation approach to synthesis problems: An algebraic analysis viewpoint II. Internal Stabilization
    • A. QUADRAT, The fractional representation approach to synthesis problems: An algebraic analysis viewpoint II. Internal Stabilization, SIAM J. Control Optim., 42 (2003), pp. 300-320.
    • (2003) SIAM J. Control Optim. , vol.42 , pp. 300-320
    • Quadrat, A.1
  • 34
    • 85052272672 scopus 로고    scopus 로고
    • On a generalization of the Youla-Kučera parametrization: I. The fractional ideals approach to SISO systems
    • to appear
    • A. QUADRAT, On a generalization of the Youla-Kučera parametrization: I. The fractional ideals approach to SISO systems, Systems Control Lett., to appear.
    • Systems Control Lett.
    • Quadrat, A.1
  • 35
    • 1842421713 scopus 로고    scopus 로고
    • An introduction to internal stabilization of linear infinite dimensional systems
    • Control of Distributed Parameter Systems: Theory and Applications, Ecole Centrale de Lille, Lille, France
    • A. QUADRAT, An introduction to internal stabilization of linear infinite dimensional systems, "Control of Distributed Parameter Systems: Theory and Applications," Proceedings of the International School in Automatic Control of Lille, Ecole Centrale de Lille, Lille, France, 2002.
    • (2002) Proceedings of the International School in Automatic Control of Lille
    • Quadrat, A.1
  • 37
    • 84972505239 scopus 로고
    • Sur la cohérence de certains anneaux de fonctions
    • J.-P. ROSAY, Sur la cohérence de certains anneaux de fonctions, Illinois J. Math., 21 (1977), pp. 895-897.
    • (1977) Illinois J. Math. , vol.21 , pp. 895-897
    • Rosay, J.-P.1
  • 40
    • 0026732287 scopus 로고
    • Algebraic geometric aspects of feedback stabilization
    • S. SHANKAR AND V. R. SULE, Algebraic geometric aspects of feedback stabilization, SIAM J. Control Optim., 30 (1992), pp. 11-30.
    • (1992) SIAM J. Control Optim. , vol.30 , pp. 11-30
    • Shankar, S.1    Sule, V.R.2
  • 41
    • 0009274368 scopus 로고
    • Noetherian Banach algebras are finite dimensional
    • A. M. SINCLAIR AND A. W. TULLO, Noetherian Banach algebras are finite dimensional, Math. Ann., 211 (1974), pp. 151-153.
    • (1974) Math. Ann. , vol.211 , pp. 151-153
    • Sinclair, A.M.1    Tullo, A.W.2
  • 42
    • 0001260901 scopus 로고
    • Faisceaux algébriques cohérents
    • J. P. SERRE, Faisceaux algébriques cohérents, Ann. of Math., 61 (1955), pp. 197-278.
    • (1955) Ann. of Math. , vol.61 , pp. 197-278
    • Serre, J.P.1
  • 43
    • 0024731675 scopus 로고
    • On stabilization and the existence of coprime factorizations
    • M. C. SMITH, On stabilization and the existence of coprime factorizations, IEEE Trans. Automat. Control, 34 (1989), pp. 1005-1007.
    • (1989) IEEE Trans. Automat. Control , vol.34 , pp. 1005-1007
    • Smith, M.C.1
  • 44
    • 0028539247 scopus 로고    scopus 로고
    • Feedback stabilization over commutative rings: The matrix case
    • V. R. SULE, Feedback stabilization over commutative rings: The matrix case, SIAM J. Control Optim., 32 (1994), pp. 1675-1695; Corrigendum, 36 (1998), pp. 2194-2195.
    • (1994) SIAM J. Control Optim. , vol.32 , pp. 1675-1695
    • Sule, V.R.1
  • 45
    • 0028539247 scopus 로고    scopus 로고
    • V. R. SULE, Feedback stabilization over commutative rings: The matrix case, SIAM J. Control Optim., 32 (1994), pp. 1675-1695; Corrigendum, 36 (1998), pp. 2194-2195.
    • (1998) Corrigendum , vol.36 , pp. 2194-2195
  • 46
    • 59749102946 scopus 로고
    • Vector bundles and projective modules
    • R. G. SWAN, Vector bundles and projective modules, Trans. Amer. Math. Soc., 105 (1962), pp. 264-277.
    • (1962) Trans. Amer. Math. Soc. , vol.105 , pp. 264-277
    • Swan, R.G.1
  • 47
    • 84966202933 scopus 로고
    • Extension problem to an invertible matrix
    • V. TOLOKONNIKOV, Extension problem to an invertible matrix, Proc. Amer. Math. Soc., 117 (1993), pp. 1023-1030.
    • (1993) Proc. Amer. Math. Soc. , vol.117 , pp. 1023-1030
    • Tolokonnikov, V.1
  • 51
    • 0040399032 scopus 로고
    • On commutative indecomposable coherent regular rings
    • Z. YICAI, On commutative indecomposable coherent regular rings, Comm. Algebra, 20 (1992), pp. 1389-1394.
    • (1992) Comm. Algebra , vol.20 , pp. 1389-1394
    • Yicai, Z.1
  • 52
    • 0019559036 scopus 로고
    • Feedback and optimal sensitivity: Model reference transformations, multiplicative seminorms, and approximate inverses
    • G. ZAMES, Feedback and optimal sensitivity: Model reference transformations, multiplicative seminorms, and approximate inverses, IEEE Trans. Automat. Control, 26 (1981), pp. 301-320.
    • (1981) IEEE Trans. Automat. Control , vol.26 , pp. 301-320
    • Zames, G.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.