Exact observability of diagonal systems with a one-dimensional output operator

Birgit Jacob; Hans Zwart

International Journal of Applied Mathematics and Computer Science (2001)

  • Volume: 11, Issue: 6, page 1277-1283
  • ISSN: 1641-876X

Abstract

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In this paper equivalent conditions for exact observability of diagonal systems with a one-dimensional output operator are given. One of these equivalent conditions is the conjecture of Russell and Weiss (1994). The other conditions are given in terms of the eigenvalues and the Fourier coefficients of the system data.

How to cite

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Jacob, Birgit, and Zwart, Hans. "Exact observability of diagonal systems with a one-dimensional output operator." International Journal of Applied Mathematics and Computer Science 11.6 (2001): 1277-1283. <http://eudml.org/doc/207555>.

@article{Jacob2001,
abstract = {In this paper equivalent conditions for exact observability of diagonal systems with a one-dimensional output operator are given. One of these equivalent conditions is the conjecture of Russell and Weiss (1994). The other conditions are given in terms of the eigenvalues and the Fourier coefficients of the system data.},
author = {Jacob, Birgit, Zwart, Hans},
journal = {International Journal of Applied Mathematics and Computer Science},
keywords = {unbounded observation operator; Hautus test; exact observability; infinite-dimensional systems; Lyapunov equation},
language = {eng},
number = {6},
pages = {1277-1283},
title = {Exact observability of diagonal systems with a one-dimensional output operator},
url = {http://eudml.org/doc/207555},
volume = {11},
year = {2001},
}

TY - JOUR
AU - Jacob, Birgit
AU - Zwart, Hans
TI - Exact observability of diagonal systems with a one-dimensional output operator
JO - International Journal of Applied Mathematics and Computer Science
PY - 2001
VL - 11
IS - 6
SP - 1277
EP - 1283
AB - In this paper equivalent conditions for exact observability of diagonal systems with a one-dimensional output operator are given. One of these equivalent conditions is the conjecture of Russell and Weiss (1994). The other conditions are given in terms of the eigenvalues and the Fourier coefficients of the system data.
LA - eng
KW - unbounded observation operator; Hautus test; exact observability; infinite-dimensional systems; Lyapunov equation
UR - http://eudml.org/doc/207555
ER -

References

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  1. Avdonin S.A. and Ivanov S.A. (1995): Families of Exponentials: The Method of Moments in Controllability Problems for Distributed Parameter Systems. — Cambridge: Cambridge University Press. Zbl0866.93001
  2. Curtain R.F. and Zwart H. (1995): An Introduction to Infinite-Dimensional Linear Systems Theory. — New York: Springer. Zbl0839.93001
  3. Garnett J.B. (1981): Bounded Analytic Functions. — New York: Academic Press. Zbl0469.30024
  4. Grabowski P. (1990): On the spectral-Lyapunov approach to parametric optimization of distributed parameter systems. — IMA J. Math. Contr. Inf., Vol.7, No.4, pp.317–338. Zbl0721.49006
  5. Grabowski P. and Callier F.M. (1996): Admissible observation operators, semigroup criteria of admissibility. — Int. Eqns. Oper. Theory, Vol.25, No.2, pp.182–198. Zbl0856.93021
  6. Jacob B. and Zwart H. (1999): Equivalent conditions for stabilizability of infinitedimensional systems with admissible control operators. — SIAM J. Contr. Optim., Vol.37, No.5, pp.1419–1455. Zbl0945.93018
  7. Jacob B. and Zwart H. (2000a): Disproof of two conjectures of George Weiss. — Memorandum 1546, Faculty of Mathematical Sciences, University of Twente. 
  8. Jacob B. and Zwart H. (2000b): Exact controllability of C0 -groups with one-dimensional input operators, In: Advances in Mathematical Systems Theory. A volume in Honor of Diederich Hinrichsen (F. Colonius, U. Helmke, D. Prätzel-Wolters and F. Wirth, Eds.). — Boston: Birkhäuser. 
  9. Jacob B. and Zwart H. (2001): Exact observability of diagonal systems with a finitedimensional output operator. — Syst. Contr. Lett., Vol.43, No.2, pp.101–109. Zbl0978.93010
  10. Komornik V. (1994): Exact controllability and stabilization. The multiplier method. Chichester: Wiley; Paris: Masson. Zbl0937.93003
  11. Nikol’skiĭ N.K. and Pavlov B.S. (1970): Bases of eigenvectors of completely nonunitary contractions and the characteristic function. — Math. USSR-Izvestija, Vol.4, No.1, pp.91–134. 
  12. Rebarber R. and Weiss G. (2000): Necessary conditions for exact controllability with a finite-dimensional input space. — Syst. Contr. Lett., Vol.40, No.3, pp.217–227. Zbl0985.93028
  13. Russell D.L. and Weiss G. (1994): A general necessary condition for exact observability. — SIAM J. Contr. Optim., Vol.32, No.1, pp.1–23. Zbl0795.93023
  14. Weiss G. (1988): Admissibility of input elements for diagonal semigroups on l 2 . — Syst. Contr. Lett., Vol.10, No.1, pp.79–82. Zbl0634.93046
  15. Zwart H. (1996): A note on applications of interpolations theory to control problems of infinite-dimensional systems. — Appl. Math. Comp. Sci., Vol.6, No.1, pp.5–14. Zbl0846.93053

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