. Xu, Controller For Infinite-dimensional systems (11) where [ fiRol(r)Forany Rn+0,etARo= 0fort 2 ma:c{l lm1,tlm2]}' so the semigroup etl, is not holomorphic using Proposition 1, it has been prlrr"d thut et(As+Aa) is expànentially stable for each set of positive physical para.-eters. From (11), one can verify that the output operator C : H + IR with 'c f =/z(0) is er-ad*irrible. Hence thL operator c is also (45 *,4e)-admissible under th; bo;ded perturbation, Quelques Remarques Sur la Stabilité et L'Observabilité 4.2. MainResult 4. A Robust Pl we can find that c(A*Au)-'tf ]=-ffi.#i where h(x) =, 0t -2ar I s'(lr-",ù l2(a1ae * 1)(o1 -Pr)l I prz2o(qr"r') g(x) = a1 -B1e'(lr-or, 1993.

H. H. Abed-j, Local feedback stabilization and bifurcation control, I. Hopf bifurcation, Systems & Control Letters, vol.7, issue.1, pp.11-17
DOI : 10.1016/0167-6911(86)90095-2

A. Bacciotti-p, Boieri Linear stabilizability of planar nonlinear systems Mathematics of control signals and systems, pp.183-193

W. Boothby-r, Marino Feedback stabilization of planar nonlinear systerns Systems & Control Letters, pp.92-1989

G. Bornard, N. Couenne, and F. , Celle Regularly persistent obsertters for bili'near sïs' tems New trends in Nonlinear control Theory, 1989.

R. W. Brockett, Differential Geometric Control Theory, chapter Asymptotic stability and feedback stabilization, pp.181-191, 1983.

A. Cima and J. , Llibre Algebric and Topological Classification of the Homogeneous Cubic Vector Fields in the plane, Jounral of Mathematical Analysis anil Applications, 1990.

R. Chabour and H. Hammouri, Stabilization of planar bilinear systems using an observer configuration, Applied Mathematics Letters, vol.6, issue.1, pp.7-10, 1993.
DOI : 10.1016/0893-9659(93)90137-C

R. Chabour and J. C. Vivalda, Stabilisation des systèmes bilinéaires dans le plan, C.n Acad.Sci.Paris, issue.312, pp.1017-1020, 1991.

R. Chabour and H. Jerbi, Stabilization of planar bilinear systems using an observer configuration, Applied Mathematics Letters, vol.6, issue.1, p.994
DOI : 10.1016/0893-9659(93)90137-C

W. P. Dayawansa, C. F. Martin, and G. Knowles, Asymptotic stabilization of a class of smooth t o-âim"*ionol systerns, SIAM J. Control and Optimization, issue.28, pp.1321-1349, 1990.

F. and J. C. Ig72, Dynatnic behauior o! processes

J. P. Gauthier and G. Bornard, outils et mod,èles mathématiques pour I,outomatique et la théorie ilu signal, chapter Stabilisation des systèmes non linéaires, pp.307-324, 1981.

J. P. Gauthier-y, Kupka A separotion principle for bilinear systems with ilissipa- tiaedrift^paraîtredansSystems&ControlLetters

O. M. Grasselli and A. Isidori, Deterministi.c state reconstruction and reachability of bilinear control Processes JACC, pp.423-427, 1977.

W. Hahn, Stabilitv of Motion, 1967.

M. A. Ha, H. Mmami, and . Jerbi, on the stabilisation of Homogeneous cubic vector Fiekts i.n the Plane

R. Herma, A. J. Nn, and . Krener, Nonlinear controllability and observability, IEEE Transactions on Automatic Control, vol.22, issue.5, pp.728-740, 1977.
DOI : 10.1109/TAC.1977.1101601

. Hamadi, M. A. Jerbi, . Ha, and J. C. Rrmami, Vivalda On the Stabilization of Homo' ' ' g"orous Afi,ne systemssoumis à 2nd, IEEE MEDITEhRANEAN SYMPOSIUM ON NEW DIRE:CnrcMS /N CONTROL k, AUTOMATION Juin, pp.19-22, 1994.

J. P. Jurdjevic and . Quinn, controllability and stability-Joum'al of Differenti'al Equations, pp.381-389, 1978.

M. Kawski, Stabilization of nonlinea.r systems in the plane, Systerns E Control Letters, issue.12, pp.169-175, 1990.

T. Kobayashi, A digital Pl-controller for distributed pa, 1988.

J. La, S. Salle, and . Lefschetz, Stab;Iity by Liapunoa's ilirect method, with applications, 1961.

R. Outbib and G. Sallet, Stabilizability of the angular velocity of a rigid body revisited. Systerns I Control Letters, pp.93-98, 1992.

S. Pohjolainen, Robust controllerfor systems with exponentially stable strongly continuous semigroups Jounral of Mathematical Analysis anil Applica' tions, voI, pp.622-636, 1985.

G. Salet, Adda Controllability for finite fa,milies of linear vector fields in the plane, RAIfuO APII, vol.21, pp.377-390, 1990.

E. D. Sontag, Feedback stabilization of nonlinear systems. ln Robust Control of Linear Systems and Nonlinear Control, pp.61-81, 1990.

E. D. Sontag, On the Observability of Polynomial Systems, I: Finite-Time Problems, SIAM Journal on Control and Optimization, vol.17, issue.1, pp.139-151, 1979.
DOI : 10.1137/0317011

H. Sussmann, Single-input obsertsability of continuous-tirne systems Math. Systems Theory, pp.263-284, 1979.

H. Sussmann, Subanalytic sets anil feedbacls control, Journal of Differential Equations, issue.31, pp.31-52, 1978.
DOI : 10.1016/0022-0396(79)90151-7

URL : https://doi.org/10.1016/0022-0396(79)90151-7

X. , C. 2. Gauthier, and J. P. , Analyse et commande d'un échangeur thermique à contre-courant. nAInO APPII, pp.377-396, 1991.

X. , C. 2. , and H. Jerbi, A Robust Pl-Controller For Infinite-dimensional Systems, International Journal of Control