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.
@article{bwmeta1.element.bwnjournal-article-amcv11i6p1277bwm,
author = {Jacob, Birgit and Zwart, Hans},
title = {Exact observability of diagonal systems with a one-dimensional output operator},
journal = {International Journal of Applied Mathematics and Computer Science},
volume = {11},
year = {2001},
pages = {1277-1283},
zbl = {1031.93065},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-amcv11i6p1277bwm}
}
Jacob, Birgit; Zwart, Hans. Exact observability of diagonal systems with a one-dimensional output operator. International Journal of Applied Mathematics and Computer Science, Tome 11 (2001) pp. 1277-1283. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-amcv11i6p1277bwm/
[000] 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. | Zbl 0866.93001
[001] Curtain R.F. and Zwart H. (1995): An Introduction to Infinite-Dimensional Linear Systems Theory. — New York: Springer. | Zbl 0839.93001
[002] Garnett J.B. (1981): Bounded Analytic Functions. — New York: Academic Press. | Zbl 0469.30024
[003] 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. | Zbl 0721.49006
[004] 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. | Zbl 0856.93021
[005] 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. | Zbl 0945.93018
[006] Jacob B. and Zwart H. (2000a): Disproof of two conjectures of George Weiss. — Memorandum 1546, Faculty of Mathematical Sciences, University of Twente.
[007] 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.
[008] 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. | Zbl 0978.93010
[009] Komornik V. (1994): Exact controllability and stabilization. The multiplier method. Chichester: Wiley; Paris: Masson. | Zbl 0937.93003
[010] 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.
[011] 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. | Zbl 0985.93028
[012] 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. | Zbl 0795.93023
[013] Weiss G. (1988): Admissibility of input elements for diagonal semigroups on l 2 . — Syst. Contr. Lett., Vol.10, No.1, pp.79–82. | Zbl 0634.93046
[014] 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. | Zbl 0846.93053