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Dualities for linear control differential systems with infinite matrices

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Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
Infinite-dimensional linear dynamic systems described by infinite matrices are studied. Approximate controllability for systems with lower-diagonal matrices is investigated, whereas observability is studied for systems with row-finite and upper-diagonal matrices. Different necessary or sufficient conditions of approximate controllability and observability of such systems are given. They are used to show dualities between these properties. The theorems on dualities extend the results known for finite-dimensional systems.
Rocznik
Strony
887--904
Opis fizyczny
Bibliogr. 27 poz.
Twórcy
autor
  • Institute of Mathematics and Physics, Białystok Technical University, Wiejska 45A, 15-351 Białystok, Poland, admoz@w.tkb.pl
Bibliografia
  • BANACH, S. (1932) Théorie des opérations linéaires. Warsaw.
  • BARTOSIEWICZ, Z. and MOZYRSKA, D. (2001) Observability of infinite-dimensional finitely presented discrete-time linear systems. Zeszyty Naukowe Politechniki Białostockiej. Matematyka-Fizyka-Chemia 20 5-14.
  • BARTOSIEWICZ, Z. and MOZYRSKA, D. (2005) Observability of row-finite countable systems of linear differential equations. Proceedings of 16th IFAC Congress. 4-8 July, Prague.
  • COOKE, R.G. (1950) Infinite Matrices and Sequence Spaces. London.
  • CURTAIN, R.F. and PRITCHARD, A.J. (1978) Infinite Dimensional Linear Systems Theory. Springer-Verlag, Berlin.
  • DEIMLING, R. (1977) Ordinary Differential Equations in Banach Spaces. Lecture Notes in Mathematics 596, Springer-Verlag.
  • EDWARDS, R.E. (1965) Functional Analysis: Theory and Applications. Holt, Rinehart & Winston.
  • FLIESS, M. ET AL. (1997) On nonlinear controllability, infinite jets and prolongations. In: Proceedings of European Control Conference ECC-97, Brussels, Belgium, July.
  • HERZOG, G. (1998) On Lipschitz conditions for ordinary differential equations in Fréchet spaces. Czech. Math. J. 48, 95-103.
  • JAKUBCZYK, B. (1992) Remarks on equivalence and linearization of nonlinear systems. In: Proc. Nonlinear Control Systems Design Symposium. Bordeaux, France.
  • KANTOROVICH, L.V. and AKILOV, G.P. (1982) Functional Analysis. Pergamon Press Ltd., Second Edition.
  • KELLEY, J.L. (1955) General Topology. Van Nostrand.
  • KLAMKA, J. (1991) Controllability of Dynamical Systems. PWN-Polish Scientific Publishers in co-edition with Kluwer Academic Publishers, Warsaw.
  • KOWALSKI, K. and STEEB, W-H. (1991) Nonlinear Dynamical Systems and Carleman Linearization. World Scientific Publishing Co. Pte. Ltd., Singapore.
  • LEMMERT, R. (1986) On ordinary differential equations in locally convex spaces. Nonlinear Anal. 10, 1385-1390.
  • MOSZYŃSKI, K. and POKRZYWA, A. (1974) Sur les systémes infinis d’equations différeritielles ordinaires dans certain espaces de Fréchet. Dissert. Math. 115.
  • MOZYRSKA, D. and BARTOSIEWICZ, Z. (2000) Local observability of systems on R∞. In: Proceedings of MTNS’2000, Perpignan, France.
  • MOZYRSKA, D. (2000) Local observability of infinitely-dimensional finitely presented dynamical systems with output (in Polish), Ph.D. thesis, Warsaw University of Technology.
  • PERSIDSKI, K.P. (1959) Countable system of differential equations and stability of their solutions (in Russian). Izv. Akad. Nauk Kazach. SSR 7, 52-71.
  • POMET, J.B. (1995) A differential geometric setting for dynamic equivalence and dynamic linearization. In: Banach Center Publications 32, 319-339.
  • ROLEWICZ, S. (1977) Functional Analysis and Control Theory, Linear Systems. PWN-Polish Scientific Publishers in co-edition with D. Reidel Publishing Company, Warsaw.
  • RUIZ, J. (1993) The Basic Theory of Power Series. Vieweg.
  • TAYLOR, A.E. and LAY, B.C. (1980) Introduction to Functional Analysis. Wiley.
  • TRIGGIANI, R. (1975) On the lack of exact controllablity for mild solutions in Banach spaces, Journal of Mathematical Analysis and Applications 50, 438-446.
  • WlLANSKY, A. and ZELLER, K. (1955) Inverses of matrices and matrix transformations, Proc. American Math. Soc. 30, 123-7.
  • ZAUTYKOV, O.A. (1965) Countable systems of differential equations and their applications (in Russian), Diff. Uravn. 1, 162-170.
  • ZAUTYKOV, O.A. and VALEEV, K.G. (1974) Infinite systems of differential equations (in Russian), Izdat. “Nauka” Kazach. SSR, Alma-Ata.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-article-BAT5-0014-0028
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