Control norms for large control times

Sergei Ivanov

ESAIM: Control, Optimisation and Calculus of Variations (1999)

  • Volume: 4, page 405-418
  • ISSN: 1292-8119

How to cite


Ivanov, Sergei. "Control norms for large control times." ESAIM: Control, Optimisation and Calculus of Variations 4 (1999): 405-418. <>.

author = {Ivanov, Sergei},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
keywords = {Controllability; families of exponentials; biorthogonal functions; Riesz bases},
language = {eng},
pages = {405-418},
publisher = {EDP Sciences},
title = {Control norms for large control times},
url = {},
volume = {4},
year = {1999},

AU - Ivanov, Sergei
TI - Control norms for large control times
JO - ESAIM: Control, Optimisation and Calculus of Variations
PY - 1999
PB - EDP Sciences
VL - 4
SP - 405
EP - 418
LA - eng
KW - Controllability; families of exponentials; biorthogonal functions; Riesz bases
UR -
ER -


  1. [1] M. Asch and G. Lebeau, Geometrical aspects of exact boundary controllability for the wave equation - a numerical study. ESAIM: Contr., Optim. Cal. Var. 3 ( 1998) 163-212. Zbl1052.93501MR1624783
  2. [2] S. Avdonin and S. Ivanov, Families of Exponentials. The Method od Moments in Controllability Problems for Distributed Parameter systemsCambridge University Press, N.Y. ( 1995). Zbl0866.93001MR1366650
  3. [3] S.A. Avdonin, M.I. Belishev and S.A. Ivanov, Controllability in filled domain for the multidimensional wave equation with singular boundary control. Zap. Nauchn. Sem. Leningrad. Otdel. Mat. Inst. Steklov. (LOMI) 210 ( 1994) 7-21. Zbl0870.93004MR1334739
  4. [4] S.A. Avdonin, S.A. Ivanov and D.L. Russell, Exponential bases in Sobolev spaces in control and observation problems for the wave equation. Proc. Roy. Soc. Edinburgh (to be submitted). Zbl0935.35014
  5. [5] C. Bardos, G. Lebeau and J. Rauch, Sharp sufficient conditions for the observation, control and stabilization of waves from the boundary. SIAM J. Control Theor. Appl. 30 ( 1992) 1024-1095. Zbl0786.93009MR1178650
  6. [6] H.O. Fattorini, Estimates for sequences biorthogonal to certain complex exponentials and boundary control of the wave equation, Springer, Lecture Notes in Control and Information Sciences 2 ( 1979). Zbl0379.93030MR490213
  7. [7] R. Glowinski, C.-H. Li and J.-L. Lions, A numerical approach to the exact controllability of the wave equation. (I) Dirichlet controls: description of the numerical methods. Japan J. Appl. Math. 7 ( 1990) 1-76. Zbl0699.65055MR1039237
  8. [8] F. Gozzi and P. Loreti, Regularity of the minimum time function and minimum energy problems: the linear case. SIAM J. Control Optim. (to appear). Zbl0958.49014MR1691938
  9. [9] W. Krabs, On Moment Theory and Controllability of one-dimensional vibrating Systems and Heating Processes, Springer, Lecture Notes in Control and Information Sciences 173 ( 1992). Zbl0955.93501MR1162111
  10. [10] W. Krabs, G. Leugering and T. Seidman, On boundary controllability of a vibrating plate. Appl. Math. Optim. 13 ( 1985) 205-229. Zbl0596.49025MR806626
  11. [11] I. Lasiecka, J.-L. Lions and R. Triggiani, Nonhomogeneous boundary value problems for second order hyperbolic operators. J. Math. Pures Appl. 65 ( 1986) 149-192. Zbl0631.35051MR867669
  12. [12] J.-L. Lions, Contrôviabilité exacte, stabilisation et perturbation des systèmes distribués, Masson, Paris Collection RMA 1 ( 1988). 
  13. [13] N.K. Nikol'skiĭ, A Treatise on the Shift Operator, Springer, Berlin ( 1986). MR827223
  14. [14] D.L. Russell, Controllability and stabilizability theory for linear partial differential equations: Recent progress and open questions. SIAM Rev. 20 ( 1978) 639-739. Zbl0397.93001MR508380
  15. [15] T.I. Seidman, The coefficient map for certain exponential sums. Nederl. Akad. Wetensch. Proc. Ser. A 89 (= Indag. Math. 48) ( 1986) 463-468. Zbl0627.42002MR869762
  16. [16] T.I. Seidman, S.A. Avdonin and S.A. Ivanov, The "window problem" for complex exponentials. Fourier Analysis and Applications (to appear). Zbl0960.42012
  17. [17] D. Tataru, Unique continuation for solutions of PDE's; between Hörmander's theorem and Holmgren's theorem. Comm. PDE 20 ( 1995) 855-884. Zbl0846.35021MR1326909

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