Admissibilité de l'observation pour des systèmes bilinéaires contrôlés par des opérateurs non bornés

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1. [1] H. Amann, Linear and Quasilinear Parabolic Problems, Birkhäuser, 1995. Zbl0819.35001MR1345385
2. [2] B. Amir, M.Y. ElBoukfaoui, A. Idrissi and L. Maniar, Admissibility of controle operators for bilinear systems. Semesterbericht Funktionalanalysis, Sommersemester, Tübingen (1998), . 
3. [3] A. Benbrik, Contrôle optimal des systèmes à paramètres répartis bilinéaires, Doctorat, Perpignan 1987. 
4. [4] H. Brezis, Opérateurs Maximaux Monotones et Semi-groupes de Contractions dans les Espaces de Hilbert, North Holland1973. Zbl0252.47055MR348562
5. [5] P.L. Butzer and H. Berens, Semigroups of Operators and Approximation, Springer-Verlag1967. Zbl0164.43702MR230022
6. [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 control7 (1997), 439 - 476. Zbl0815.93046MR1472401
7. [7] R.F. Curtain and A.J. Pritchard, Infinite Dimensional Linear System Theory, Lecture Notes in Control and Information Sciences8Springer-Verlag, 1978. Zbl0389.93001MR516812
8. [8] -----, An abstract theory for unbounded control action for distributed parameter systems, SIAM J. Control and Opt.15 (1977), 566 - 611. Zbl0359.93021MR476057
9. [9] R.F. Curtain and G. Weiss, Well posedness of triples of operators (in the sense of linear systems theory), International Series of Numerical Mathematics91Birkhäuser-Verlag, (1989), 41 - 58. Zbl0686.93049MR1033051
10. [10] G. Da Pratoand P. Grisvard, Maximal regularity for evolution equations by interpolation and extrapolation, J. Funct. Anal.58, (1984), 107 - 124. Zbl0593.47041MR757990
11. [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.116Marcel Dekker, 1989, 125 - 152. Zbl0701.47021MR1009392
12. [12] N. ElAlami, Analyse et commande optimale des systèmes bilinéaires distribués, application aux procédés energétiques, Doctorat d'Etat-I.M.P. Perpignan 1986. 
13. [13] K.J. Engel and R. Nagel, One-parameter Semigroups for Linear Evolution Equations, Springer-Verlag, 1999. Zbl0952.47036MR1721989
14. [14] H.O. Fattorini, Boundary control systems, SIAM J. Control6 (1968) , 349 - 385. Zbl0164.10902MR239249
15. [15] D. Hinrichsen and A.J. Pritchard, Robust stability of linear evolution operators on Banach spaces, SIAM J. Cont. Optim.32 (1994), 1503 - 1541. Zbl0817.93055MR1297095
16. [16] A. Idrissi and A. Rhandi, Admissibility of time-varying observation for non-autonomous systems, Semesterbericht Funktionalanalysis, Sommersemester, Tübingen, (1999). Zbl1123.93302
17. [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. Zbl0839.93057MR1343339
18. [18] B.V. Keulen, H∞-Control for Distributed Parameter Systems: a State-Space Approach, Birkhäuser, 1993. Zbl0788.93018MR1269323
19. [19] J.L. Lions, Optimal Control of Systems Gouverned by Partial Differential Equations, Springer-Verlag, New York, 1971. Zbl0203.09001
20. [20] L. Maniar and A. Rhandi, Extrapolation and inhomogeneous retarded differential equations in infinite dimensional Banach spaces, Rend. Circ. Mat. Palermo47 (1998), 331 - 346. Zbl0916.34065MR1633503
21. [21] R. Nagel, Sobolev spaces and semigroups, Semesterberichte Funktionalanalysis, Sommersemester, Tübingen, (1983). 
22. [22] R. Nagel, G. Nickel and S. Romanelli, Identification of extrapolation spaces for unbounded operators, Tübinger Berichte Zur Funktionalanalysis (1995), Tübingen. Zbl0863.47024MR1390474
23. [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. Zbl0790.45011MR1241671
24. [24] A. Pazy, Semigroups of Linear Operators and Applications to Partial Differential Equations, Springer-Verlag, 1983. Zbl0516.47023MR710486
25. [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 Information2 (1985), 335 - 362. Zbl0646.34078MR872455
26. [26] D.L. Russell, On boundary value controllability of linear symmetric hyperbolic systems, Mathematical Theory of Control, Academic Press, New York, (1967), 312 - 321. Zbl0214.39607MR258500
27. [27] -----, Quadratic performance criteria in boundary control of linear symmetric hyperbolic systems, SIAM J. Control Optim.Il (1973), 475 - 509. Zbl0237.49009MR328728
28. [28] J.M.A.M. van Neerven, The Adjoint of a Semigroup of Linear Operators, Lecture Notes Math.1529Springer-Verlag, 1992. Zbl0780.47026MR1222650
29. [29] D. Salamon, Infinite-dimensional linear systems with unbounded control and observation: a functional analytic approach, Trans. Amer. Math. Soc.300 (1987), 383 - 431. Zbl0623.93040MR876460
30. [30] G. Weiss, Admissible observation operators for linear semigroups, Israel J. Math.65 (1989), 17 - 43. Zbl0696.47040MR994732