Admissibilité de l'observation pour des systèmes bilinéaires contrôlés par des opérateurs non bornés
Annales Mathématiques Blaise Pascal, Volume 8 (2001) no. 1, pp. 73-92.
@article{AMBP_2001__8_1_73_0,
     author = {Abdelali Idrissi},
     title = {Admissibilit\'e de l'observation pour des syst\`emes bilin\'eaires contr\^ol\'es par des op\'erateurs non born\'es},
     journal = {Annales Math\'ematiques Blaise Pascal},
     pages = {73--92},
     publisher = {Laboratoires de Math\'ematiques Pures et Appliqu\'ees de l'Universit\'e Blaise Pascal},
     volume = {8},
     number = {1},
     year = {2001},
     doi = {10.5802/ambp.136},
     zbl = {0995.93042},
     mrnumber = {1863648},
     language = {fr},
     url = {https://ambp.centre-mersenne.org/articles/10.5802/ambp.136/}
}
TY  - JOUR
TI  - Admissibilité de l'observation pour des systèmes bilinéaires contrôlés par des opérateurs non bornés
JO  - Annales Mathématiques Blaise Pascal
PY  - 2001
DA  - 2001///
SP  - 73
EP  - 92
VL  - 8
IS  - 1
PB  - Laboratoires de Mathématiques Pures et Appliquées de l'Université Blaise Pascal
UR  - https://ambp.centre-mersenne.org/articles/10.5802/ambp.136/
UR  - https://zbmath.org/?q=an%3A0995.93042
UR  - https://www.ams.org/mathscinet-getitem?mr=1863648
UR  - https://doi.org/10.5802/ambp.136
DO  - 10.5802/ambp.136
LA  - fr
ID  - AMBP_2001__8_1_73_0
ER  - 
%0 Journal Article
%T Admissibilité de l'observation pour des systèmes bilinéaires contrôlés par des opérateurs non bornés
%J Annales Mathématiques Blaise Pascal
%D 2001
%P 73-92
%V 8
%N 1
%I Laboratoires de Mathématiques Pures et Appliquées de l'Université Blaise Pascal
%U https://doi.org/10.5802/ambp.136
%R 10.5802/ambp.136
%G fr
%F AMBP_2001__8_1_73_0
Abdelali Idrissi. Admissibilité de l'observation pour des systèmes bilinéaires contrôlés par des opérateurs non bornés. Annales Mathématiques Blaise Pascal, Volume 8 (2001) no. 1, pp. 73-92. doi : 10.5802/ambp.136. https://ambp.centre-mersenne.org/articles/10.5802/ambp.136/

[1] H. Amann, Linear and Quasilinear Parabolic Problems, Birkhäuser, 1995. | MR: 1345385 | Zbl: 0819.35001

[2] B. Amir, M.Y. Elboukfaoui, A. Idrissi and L. Maniar, Admissibility of controle operators for bilinear systems. Semesterbericht Funktionalanalysis, Sommersemester, Tübingen (1998), .

[3] A. Benbrik, Contrôle optimal des systèmes à paramètres répartis bilinéaires, Doctorat, Perpignan 1987.

[4] H. Brezis, Opérateurs Maximaux Monotones et Semi-groupes de Contractions dans les Espaces de Hilbert, North Holland 1973. | MR: 348562 | Zbl: 0252.47055

[5] P.L. Butzer and H. Berens, Semigroups of Operators and Approximation, Springer-Verlag 1967. | MR: 230022 | Zbl: 0164.43702

[6] R.F. Curtain, H. Logemann, S. Townley and H. Zwart, Well-posedness, stabilizability and admissibility for Pritchard Salamon systems, J. Math. Systems, Estimation and control 7 (1997), 439 - 476. | MR: 1472401 | Zbl: 0815.93046

[7] R.F. Curtain and A.J. Pritchard, Infinite Dimensional Linear System Theory, Lecture Notes in Control and Information Sciences 8 Springer-Verlag, 1978. | MR: 516812 | Zbl: 0389.93001

[8] -----, An abstract theory for unbounded control action for distributed parameter systems, SIAM J. Control and Opt. 15 (1977), 566 - 611. | MR: 476057 | Zbl: 0359.93021

[9] R.F. Curtain and G. Weiss, Well posedness of triples of operators (in the sense of linear systems theory), International Series of Numerical Mathematics 91 Birkhäuser-Verlag, (1989), 41 - 58. | MR: 1033051 | Zbl: 0686.93049

[10] G. Da Pratoand P. Grisvard, Maximal regularity for evolution equations by interpolation and extrapolation, J. Funct. Anal. 58, (1984), 107 - 124. | MR: 757990 | Zbl: 0593.47041

[11] W. Desch and W. Schappacher, Some generation results for perturbed semigroups, Semigroup Theory and Applications (Proceedings Trieste 1987) (P. Clément, S. Invernizzi, E. Mitidieri and I.I. Vrabie), Lec. notes in pure and Appl. 116 Marcel Dekker, 1989, 125 - 152. | MR: 1009392 | Zbl: 0701.47021

[12] N. Elalami, Analyse et commande optimale des systèmes bilinéaires distribués, application aux procédés energétiques, Doctorat d'Etat-I.M.P. Perpignan 1986.

[13] K.J. Engel and R. Nagel, One-parameter Semigroups for Linear Evolution Equations, Springer-Verlag, 1999. | MR: 1721989 | Zbl: 0952.47036

[14] H.O. Fattorini, Boundary control systems, SIAM J. Control 6 (1968) , 349 - 385. | MR: 239249 | Zbl: 0164.10902

[15] D. Hinrichsen and A.J. Pritchard, Robust stability of linear evolution operators on Banach spaces, SIAM J. Cont. Optim. 32 (1994), 1503 - 1541. | MR: 1297095 | Zbl: 0817.93055

[16] A. Idrissi and A. Rhandi, Admissibility of time-varying observation for non-autonomous systems, Semesterbericht Funktionalanalysis, Sommersemester, Tübingen, (1999).

[17] B. Jacobe, V. Dragan and A.J. Pritchard, Infinite dimensional time-varying systems with nonlinear output feedback, Integr. Equat. Oper Th. 22 (1995), 440 - 462. | MR: 1343339 | Zbl: 0839.93057

[18] B.V. Keulen, H∞-Control for Distributed Parameter Systems: a State-Space Approach, Birkhäuser, 1993. | MR: 1269323 | Zbl: 0788.93018

[19] J.L. Lions, Optimal Control of Systems Gouverned by Partial Differential Equations, Springer-Verlag, New York, 1971. | Zbl: 0203.09001

[20] L. Maniar and A. Rhandi, Extrapolation and inhomogeneous retarded differential equations in infinite dimensional Banach spaces, Rend. Circ. Mat. Palermo 47 (1998), 331 - 346. | MR: 1633503 | Zbl: 0916.34065

[21] R. Nagel, Sobolev spaces and semigroups, Semesterberichte Funktionalanalysis, Sommersemester, Tübingen, (1983).

[22] R. Nagel, G. Nickel and S. Romanelli, Identification of extrapolation spaces for unbounded operators, Tübinger Berichte Zur Funktionalanalysis (1995), Tübingen. | MR: 1390474

[23] R. Nagel and E. Sinestrari, Inhomogeneous Volterra integrodifferential equations for Hille-Yosida operators, , Marcel Dekker, Lecture Notes Pure Appl. Math. 150 (1994), 51 - 70. | MR: 1241671 | Zbl: 0790.45011

[24] A. Pazy, Semigroups of Linear Operators and Applications to Partial Differential Equations, Springer-Verlag, 1983. | MR: 710486 | Zbl: 0516.47023

[25] A.J. Pritchard and D. Salamon, The linear quadratic control problem for retarded systems with delays in control and observation, IMA J. of Math. Control and Information 2 (1985), 335 - 362. | MR: 872455 | Zbl: 0646.34078

[26] D.L. Russell, On boundary value controllability of linear symmetric hyperbolic systems, Mathematical Theory of Control, Academic Press, New York, (1967), 312 - 321. | MR: 258500 | Zbl: 0214.39607

[27] -----, Quadratic performance criteria in boundary control of linear symmetric hyperbolic systems, SIAM J. Control Optim. Il (1973), 475 - 509. | MR: 328728 | Zbl: 0237.49009

[28] J.M.A.M. Van Neerven, The Adjoint of a Semigroup of Linear Operators, Lecture Notes Math.1529 Springer-Verlag, 1992. | MR: 1222650 | Zbl: 0780.47026

[29] D. Salamon, Infinite-dimensional linear systems with unbounded control and observation: a functional analytic approach, Trans. Amer. Math. Soc. 300 (1987), 383 - 431. | MR: 876460 | Zbl: 0623.93040

[30] G. Weiss, Admissible observation operators for linear semigroups, Israel J. Math. 65 (1989), 17 - 43. | MR: 994732 | Zbl: 0696.47040

Cited by Sources: