D. Aeyels, Local and global stabilizability for nonlinear systems, in Theory and appli,cat'ions of Nonli,near Control Systems, pp.93-105, 1986.

. Artstein, Stabilization with relaxed controls, Nonli,near AnaI. Theory Meth, Appl, vol.7, pp.1163-1173, 1983.
DOI : 10.1016/0362-546x(83)90049-4

A. Bacciotti, The Local Stabilizability Problem for Nonlinear Systems, IMA Journal of Mathematical Control and Information, vol.5, issue.1, pp.27-39, 1988.
DOI : 10.1093/imamci/5.1.27

S. Battilotti and W. P. Dayawansa, Noninteracting control with stability for a class of nonlinear systems, Systems & Control Letters, vol.17, issue.5, pp.327-338, 1991.
DOI : 10.1016/0167-6911(91)90131-W

S. Battilotti and \. P. Dayawansa, Stabilization of globally noninteractive nonlinea,r systems, J. Math. Sgstems Esti,mati,on and Control L, vol.4, pp.441-464, 1991.

M. Bensoubaya, A. Ferfera, and A. Iggidr, Stabilisation de systèmes non linéaires discrets, C.R. Acad. Sci, pp.37-374, 1995.

M. Bensoubaya, A. Ferfera, and A. Iggidr, On the stabilization of continuous and discrete time nonlinear systems, communication présentée à la 2ème Conférence Intemati,onale de Marrakesh sur les équati,ons différenti,elles, pp.6-20

M. Bensoubaya, A. Ferfera, and A. Iggidr, Stabilisation globale de systèmes non linéaires stochastiques, C.R. Acad. Sci, pp.427-432, 1996.

M. Bensoubaya, A. Ferfera, and A. Iggidr, Global stabilization of nona.fHne control systems, Proc. IASTED Internati,onal Conference MODELING, pp.7-19

R. W. Brockett, Asymptotic stability and feedback stabilization, Di,fferenti,al Geometric Control Theory, pp.181-191, 1983.

C. Byrnes and A. Isidori, A frequency domain philosophy for nonlinea,r systems with applications to stabilization and to adaptive control, Proc. 23rd, IEEE Conf. Dec. Contr, pp.1569-573, 1984.

C. Byrnes and A. Isidori, Global feedback stabilization of nonlinear minimum phase systems, Proc. 24th IEEE Conf. Dec. Contr., Ft. Lauderdale, pp.1031-1037, 1985.

C. Byrnes and A. Isidori, Local stabilization of minimum-phase nonlinear systems, Systems & Control Letters, vol.11, issue.1, pp.9-16, 1988.
DOI : 10.1016/0167-6911(88)90105-3

C. Byrnes and A. Isidori, New results and examples in nonlinear feedback stabilization , Sgst, Contr. Lett. L2, pp.437-442, 1939.

C. Byrnes and \. Lin, Losslessness, feedback equivalence, and the global stabilization of discrete-time nonlinear systems, IEEE Transactions on Automatic Control, vol.39, issue.1, pp.39-83, 1994.
DOI : 10.1109/9.273341

C. Byrnes, W. Lin, and B. K. Ghosh, Stabilization of discrete-time nonlinear systems by smooth state feedback, Syst. Contr. Lett. 2L, pp.255-263, 1993.
DOI : 10.1016/0167-6911(93)90036-6

R. Chabour and A. Ferfera, Noninteracting control and disturbance decoupling with singnlarity for two dimensional bilinea,r systems, J. Math. Systems Estimati,on, pp.429-444, 1992.

R. Chabour and A. Ferfera, Singularity for static-state feedback linearizable bilinear systems, IEEE Transactions on Automatic Control, vol.44, issue.8, 1997.
DOI : 10.1109/9.780421

R. Chabour and A. Ferfera, Noninteracting control with singularity for a class of bilinear systems, Nonli,near Anal, Theory Meth, Appl

R. Chabour and P. Florchinger, A remark on the stabilisation of planar control differential equations corrupted by an additive noise, 31st IEEE Conf

R. Chabour and P. Florchinger, Exponential mean squaxe stability of pa,rtially linear stochastic systems, Appli, Math.s Lett, vol.63, pp.91-95, 1993.

R. Chabour and P. Florchinger, Stabilization of planar control bilinear equations corrupted by an additive noise, Proc. Znd Eur.Conf Contr, 1993.

R. Chabour and M. Oumoun, A stochastic version of Jurdjevic-Quinn theorem, J. Stoch. Anal

R. Chabour and M. Oumoun, On a universal formula for the stabilization of control stochastic nonlinear systems, Stochastic Analysis and Applications, vol.16, issue.3
DOI : 10.1016/0167-6911(89)90028-5

R. Chabour, G. Sallet, and J. C. Vivalda, Stabilization of nonlinear systems: A bilinear approach, Mathematics of Control, Signals, and Systems, vol.2, issue.3, pp.224-246, 1993.
DOI : 10.1007/BF01211621

S. T. Chung and J. W. Gfizzie, Sa,mpled-data observer error linearization, Automati, pp.26-997, 1990.

G. Cicarella, M. D. Mora, and A. Germani, Observers for discrete-time nonlinear systems, Systems & Control Letters, vol.20, issue.5, pp.373-382, 1993.
DOI : 10.1016/0167-6911(93)90016-Y

G. Cicarella, M. D. Mora, and A. Germani, A robust observer for discrete time nonlinear systems, Systems & Control Letters, vol.24, issue.4, pp.291-300
DOI : 10.1016/0167-6911(94)00021-M

D. Claude, Commande noninteractive simple des systèmes non linéaires par bouclages statiques réguliers, C. R. Acad. Sc. Paris, Série I, vol.303, pp.833-836, 1986.

D. Claude, Everything you always wanted to know about linearization, in Algebrai ,c and Geometri,c Methods i,n Nonli,near Control Theory, M. Fliess et M, pp.18-226, 1986.

J. M. Coron, A necessary condition for feedback stabilization, Systems & Control Letters, vol.14, issue.3, pp.227-232, 1990.
DOI : 10.1016/0167-6911(90)90017-O

J. M. Coron, Linearized Control Systems and Applications to Smooth Stabilization, SIAM Journal on Control and Optimization, vol.32, issue.2, pp.32-35, 1994.
DOI : 10.1137/S0363012992226867

W. P. Dayawansa, C. F. Martin, and G. Knowles, Asymptotic Stabilization of a Class of Smooth Two-Dimensional Systems, SIAM Journal on Control and Optimization, vol.28, issue.6, pp.28-32, 1990.
DOI : 10.1137/0328070

A. Ferfera and A. Iggidr, Feedback stabilization of stochastic nonlinea,r composite systems, Appli, Math. Letter, vol.7, issue.3L994, pp.45-49

A. Ferfera and A. Iggidr, A remark on the stabilization of partially linear composite systems, IEEE Transactions on Automatic Control, vol.42, issue.3, pp.4-4, 1997.
DOI : 10.1109/9.557587

M. Fliess, Un Outil Algebrique: Les Series Formelles Non Commutatives, Lect. Note Econom. Math. Syst, vol.131, pp.122-170, 1976.
DOI : 10.1007/978-3-642-48895-5_9

P. Florchinger, Stabilization of control stochastic bilinear systems by linear feedback law, Proc. SINS'9Z

P. Florchinger, A criterion for the feedback stabilization of control stochastic differential equations, [1992] Proceedings of the 31st IEEE Conference on Decision and Control
DOI : 10.1109/CDC.1992.371411

P. Florchinger, On the stabilization of homogeneous control stocha"stic systems, Proc. 32nd IEEE Conf. Dec. Contr, pp.855-856, 1993.

P. Florchinger, A universal formula for the stabilization of control stochastic differential equations, Stochastic Analysis and Applications, vol.11, issue.2, pp.155-162, 1993.
DOI : 10.1007/BF02551276

P. Florchinger, Feedback stabilization of a class of planar control stochastic bilinea ,r equations, Proc. Ùnd Eur.Conf. Contr, 1993.

P. Florchinger, A stochastic version of Jurdjevic???Quinn theorem, Stochastic Analysis and Applications, vol.12, issue.4, pp.473-480
DOI : 10.1007/BF02551276

P. Florchinger, Lyapunov-like techniques for stochastic stability, SIAM J. Contr. Opti,mi,z, vol.33, issue.1, pp.151-1169, 1995.

E. Fteund, The structure of decoupled nonlinear systems, Int. J. Contr. 2L, pp.443-450, 1975.

J. P. Gauthier and G. Bornard, Stabilisation des systèmes non linéaires, in Outi,ls et Modèles Mathémati,ques pour l'Automati,que, lAnalyse des Systèms et le Thai, pp.307-324

J. W. Grizzie, Feedback linearization of discrete-time systems, Lecture Note Contr, Inform. ^9ci, vol.83, pp.273-301, 1986.

J. W. Grizzle, Local Input-Output Decoupling of Discrete Time Nonlinear Systems, Int. J. Contr, vol.43, pp.1517-1530, 1986.
DOI : 10.1007/978-94-009-4706-1_22

J. W. Grizzle and P. E. , Newton observers and nonlinea,r discrete-time controI, Proc. 29th IEEE Conf. Dec. Contr, pp.760-767, 1990.

J. W. Grizzle and H. Nijmeijer, Zeros at infinity for nonlinear discrete time systems, Mathematical Systems Theory, vol.1, issue.1, pp.79-93, 1986.
DOI : 10.1007/978-1-4684-0068-7

I. J. Ha, The Standard Decomposed System and Noninteracting Feedback Control of Nonlinear Systems, SIAM Journal on Control and Optimization, vol.26, issue.5, pp.235-249, 1988.
DOI : 10.1137/0326067

I. J. Ha and E. G. Gilbert, A complete characterization of decoupling control laws for a general class of nonlinear systems, IEEE Trans. Automat. Contr. AC, pp.31-823, 1986.

W. Hahn, Stabi,li.tg of mot'i,on. New-York: Springer-Verlag, 1.967. [54] H. Hermes. Homogeneous coordinates and continuous stabilizing feedback controls, 1991.

H. J. Huijberts, A. J. Van-der, and . Schaft, Input-output decoupling with stability for Hamiltonian systems, Mathematics of Control, Signals and Systems, vol.2, issue.2, pp.125-138, 1990.
DOI : 10.1007/BFb0006368

A. Isidori, Nonl'inear Control Sgstems, 1989.

A. Isidori, J. \m, and . Grizzle, Fixed modes and nonlinear noninteracting control with stability, IEEE Transactions on Automatic Control, vol.33, issue.10, pp.907-914, 1988.
DOI : 10.1109/9.7244

A. Isidori, A. J. Krener, C. Gorigiorgi, and S. Monaco, Nonlinear decoupling via feedback: A differential geometric approach, IEEE Transactions on Automatic Control, vol.26, issue.2, pp.331-345, 1981.
DOI : 10.1109/TAC.1981.1102604

A. Isidori and C. H. Moog, On the nonlinear equivalent of the notion of transmission zeros, Lectures Notes in Control and Information Sciences, vol.105, 1986.
DOI : 10.1007/BFb0043181

B. Jakubczyk and W. Respondek, On linearization of control systems, Bull. Acad. Pol. Sci,. Ser. Sci,. Math, vol.28, pp.5-7, 1980.

B. Jakubczyk and E. D. Sontag, Controllability of Nonlinear Discrete-Time Systems: A Lie-Algebraic Approach, SIAM Journal on Control and Optimization, vol.28, issue.1, pp.1-33, 1990.
DOI : 10.1137/0328001

N. Kalouptsidis and J. Tsinias, Stability improvement of nonlinear systems by feedback, IEEE Transactions on Automatic Control, vol.29, issue.4, pp.364-367
DOI : 10.1109/TAC.1984.1103518

M. Kawski, Homogeneous stabilizing feedback laws, Contr. Theory Adu. Tech, vol.6, pp.497-502, 1990.

M. Kawski, Stabilization of nonlinear systems in the plane, Systems & Control Letters, vol.12, issue.2, pp.169-175, 1990.
DOI : 10.1016/0167-6911(89)90010-8

P. V. Kokotovic and H. J. Sussmann, A positive real condition for global stabilization of nonlinear systems, Systems & Control Letters, vol.13, issue.2, pp.125-133, 1989.
DOI : 10.1016/0167-6911(89)90029-7

M. A. Krasnosel-'ski and P. P. Zabreiko, Geometri,c Methods of nonli,near Analysi,s, 1984.

H. J. Kushner, Stochastic stability, Lecture Notes in Mathematics, vol.46, issue.3, pp.97-124
DOI : 10.1073/pnas.46.3.363

J. Lasalie and S. Lefschetz, Stabi,Ii,ty by Lyapunou's d'i,rect method wi,th appli,cati,ons, 1961.

H. G. Lee and S. I. Marcus, Approximate and linearizability of nonlinear discretetime systems, Int. J. Contr, vol.44, pp.3-24, 1986.

H. G. Lee and S. I. Ma, Linearization of discrete-time systems, International Journal of Control, vol.28, issue.5, pp.1803-1822, 1987.
DOI : 10.1016/S0167-6911(82)80042-X

K. K. Lee and A. Araposthathis, Rema,rks on smooth feedback stabilization of nonlinea,r systems, Syst. Contr. Lett, vol.10, pp.4-44, 1988.

W. Lin, Bounded smooth state feedback and a global separation principle for non-affine nonlinear systems, Systems & Control Letters, vol.26, issue.1, pp.41-53, 1995.
DOI : 10.1016/0167-6911(94)00109-9

W. Lin, Global stabilization of discrete non-a,ffine systems, Proc. 34th IEEE Conf. Dec. Contr, pp.510-511, 1995.

\. /. Lin, Global asymptotic stabilization of general nonlinear systems with stable free dynamics via passivity and bounded feedback, Automati, pp.915-924, 1996.

W. Lin and C. I. Byrnes, Passivity and absolute stabiiization of a class of discretetime nonlinear systems, pp.263-267, 1995.

W. Lin and C. I. Byrnes, Zero-state observability and stability of discrete-time nonlinear systems, Automatica, vol.31, issue.2, pp.269-274, 1995.
DOI : 10.1016/0005-1098(94)00088-Z

R. Marino, High-gain feedback in non-linear control systems???, International Journal of Control, vol.22, issue.931, pp.1369-1385, 1985.
DOI : 10.1080/00207178508933431

R. Marino, W. M. Boothby, and D. L. Elliott, Geometric properties of linea,rizable control systems, Math. Sgst. Theory L8, pp.97-123, 1985.

J. L. Massera, Contributions to Stability Theory, The Annals of Mathematics, vol.64, issue.1, pp.182-206, 1956.
DOI : 10.2307/1969955

S. Monaco, D. Normand-cyrot, and I. Isola, Nonlinear decoupling in discrete-time, Proc. IFAC NOLCOS'89, pp.45-48, 1989.

P. E. Moraal and J. W. Grizzle, Observer design for nonlinear systems with discrete-time measurements, IEEE Transactions on Automatic Control, vol.40, issue.3, pp.395-404, 1995.
DOI : 10.1109/9.376051

K. Nam, Linearization of discrete-time nonlinear systems and a canonical structure, IEEE Tbans. Autom. Contr, vol.34, pp.19-22, 1989.

H. Nijmeijer, Local (dynamic) Input-Output Decoupling of Discrete Time Nonlinear Systems, IMA Journal of Mathematical Control and Information, vol.4, issue.3, pp.237-250, 1987.
DOI : 10.1093/imamci/4.3.237

H. Nijmeijer and J. M. Schumacher, The regular local noninteracting control problemfornonlinearcontrolsystems, pp.232-1245

R. Outbib and G. Sallet, Stabilizability of the angular velocity of a rigid body revisited, Systems & Control Letters, vol.18, issue.2, pp.93-98, 1992.
DOI : 10.1016/0167-6911(92)90013-I

W. A. Porter, Diagonalization and inverses for nonlinear systems, Int. J. Contr, vol.1, pp.67-76, 1970.

W. Respondek, Geometric methods in linearization of control systems, Mathemati ,cal Control Theory, pp.453-467, 1985.
DOI : 10.4064/-14-1-453-467

A. Saberi, P. V. Kokotovic, and H. J. Sussmann, Global stabilization of partially linear composite systems, SIAM J. Contr. and Opti, pp.28-1491, 1990.

S. Sastry and A. Isidori, Adaptive control of linearizable systems, IEEE Transactions on Automatic Control, vol.34, issue.11, pp.1123-1131, 1989.
DOI : 10.1109/9.40741

P. Seibert and R. Suarez, Global stabilization of nonlinear cascade systems, Systems & Control Letters, vol.14, issue.4, pp.347-352, 1990.
DOI : 10.1016/0167-6911(90)90056-Z

S. N. Singh and W. J. Rugh, Decoupling in a Class of Nonlinear Systems by State Variable Feedback, Journal of Dynamic Systems, Measurement, and Control, vol.94, issue.4, pp.323-329, 1972.
DOI : 10.1115/1.3426615

P. K. Sinha, State feedback decoupling of nonlinear systems, IEEE Transactions on Automatic Control, vol.22, issue.3, pp.487-489
DOI : 10.1109/TAC.1977.1101529

E. D. Sontag, A universal construction of Artstein's theorem on nonlinea,r stabilization, Syst. Contr. Lett, vol.13, pp.7-123, 1989.

E. D. Sontag, Feedback Stabilization of Nonlinear Systems, Robust Control of Li,near Sgstems and Nonli, pp.61-81, 1990.
DOI : 10.1007/978-1-4612-4484-4_4

Y. Stepanenko and X. Yang, Stabilization analysis of discrete nonlinear systems, International Journal of Control, vol.3, issue.6, pp.1313-1326, 1995.
DOI : 10.1080/0020718508961131

R. Su, On the linear equivalents of nonlinear systems, Systems & Control Letters, vol.2, issue.1, pp.48-52, 1982.
DOI : 10.1016/S0167-6911(82)80042-X

H. J. Sussmann, Semigroup representations, bilinear approximation of inputoutput maps, and generalized inputs, Lect. Note Econom. Math. Syst. L31, vol.976, pp.7-9

H. J. Sussmann and P. V. Kokotovic, The peaking phenomenon and the global stabilization of nonlinear systems, IEEE Transactions on Automatic Control, vol.36, issue.4, pp.424-440
DOI : 10.1109/9.75101

J. Tsinias, Sufficient Lyaounov-like conditions for stabilization, pp.343-357, 1989.

J. Tsinias, Stabilizability of Discrete-Time Nonlinear Systems, IMA Journal of Mathematical Control and Information, vol.6, issue.2, pp.135-150, 1989.
DOI : 10.1093/imamci/6.2.135

J. Tsinias and N. Kalouptsidis, Output Feedback Stabilization of Discrete-Time Control Systems, IMA Journal of Mathematical Control and Information, vol.7, issue.3, pp.257-268, 1990.
DOI : 10.1093/imamci/7.3.257

M. Vidyasagar, Decomposition techniques for large-scale systems with nonadditive interactions: Stability and stabilizability, IEEE Transactions on Automatic Control, vol.25, issue.4, pp.773-779, 1980.
DOI : 10.1109/TAC.1980.1102422

K. Wagner, On nonlinear noninteraction with stability, Proceedings of the 28th IEEE Conference on Decision and Control, pp.994-1999, 1989.
DOI : 10.1109/CDC.1989.70514

R. Chabour and J. C. Vivalda, Stabilisation des systèmes bilinéaires dans le plan, C. R. Acad. Sci, pp.0-7, 1991.

D. Claude, D??couplage des Syst??mes Non Lin??aires, Series G??n??ratrices Non Commutatives et Alg??bres de Lie, SIAM Journal on Control and Optimization, vol.24, issue.3, pp.24562-578, 1986.
DOI : 10.1137/0324033

P. E. Crouch, I. Ighneiwa, and F. Lamnabhi-lagarrigue, On the singular tracking problem, Mathematics of Control, Signals, and Systems, vol.15, issue.4, pp.34-362, 1991.
DOI : 10.1007/BFb0042025

A. Glumineau, C. H. Moog, T. J. Ta, and . Rn, Interconnected Zero Dynamics in Nonlinear Systems and their Role in Dynamic Noninteracting Control with Stability, y'feu Trends i,n Sgstem Theory (Proc. Conf. Genoa, 1990.
DOI : 10.1007/978-1-4612-0439-8_39

R. M. Hirschorn, Invariant distributions and disturbance decoupling of nonlinea,r systems, SIAM J. Control Opti,mi,z, vol.19, pp.1-19, 1981.

H. J. Huijberts, A. J. Van-der, and . Schaft, Input-output decoupling with stability for Hamiltonian systems, Mathematics of Control, Signals and Systems, vol.2, issue.2, pp.125-138, 1990.
DOI : 10.1007/BFb0006368

A. Isidori, A. J. Krener, C. Gori-giorgi, and S. Monaco, Nonlinear decoupling via feedback: A differential geometric approach, IEEE Transactions on Automatic Control, vol.26, issue.2, pp.331-345, 1981.
DOI : 10.1109/TAC.1981.1102604

A. Isidori and J. W. Gfizzke, Fixed modes and nonlinear noninteracting control with stability, IEEE Transactions on Automatic Control, vol.33, issue.10, pp.907-916, 1988.
DOI : 10.1109/9.7244

K. Wagner, On nonlinear noninteraction with stability, 28th IEEE Conf, Contr. Tampa (Florida), 1989.

R. Chabour and A. Ferfera, Noninteracting control and disturbance decoupling with singularity for two dimensional bilinear systems, Journal of Mathematical Systems, Esti,mati,on and Control, vol.2, issue.4, pp.429-444, 1992.

R. Chabour, G. Sallet, and J. C. Vivalda, Stabilization of nonlinear systems: A bilinear approach, Mathematics of Control, Signals, and Systems, vol.2, issue.3, pp.224-246, 1993.
DOI : 10.1007/BF01211621

A. Glumineau, C. H. Moog, and T. J. Tarn, Interconnected zero dynamics in non- Iinear systems and their role in dynamic noninteracting Control with stability, .l{eu Tlends i,n System Theory (Proc. Conf. Genoa, 1990.

H. J. Huijberts, A. J. Van-der, and . Schafb, Input-output decoupling with stability for Hamiltonian systems, Mathematics of Control, Signals and Systems, vol.2, issue.2, pp.125-138, 1990.
DOI : 10.1007/BFb0006368

A. Isidori, Nonli,near Control Sgstems

A. Isidori and J. W. Grizz\e, Fixed modes and nonlinear noninteracting control with stability, IEEE Transactions on Automatic Control, vol.33, issue.10, pp.907-916, 1988.
DOI : 10.1109/9.7244

F. Fbrthermore, 11) one cân deduce that the zero dynamics of (3.10) are included in those of (3.2) which completes the proof of the proposition

P. V. Kokotovic and H. J. Sussmann, A positive real condition for global stabilization of nonlinear systems, Systems & Control Letters, vol.13, issue.2, pp.125-133, 1989.
DOI : 10.1016/0167-6911(89)90029-7

P. V. Kokotovic and H. J. Sussmann, The peaking Phenomenon a.nd the global Stabilization of nonlinear systems, IEEE Tbans. Automat. Control, vol.36, issue.4, pp.424-440, 1991.

J. Lasatle and S. Lefschetz, Stabi,li,tg by Lyapunou's di,rect method wi,th appli,cat'ions, 1961.

J. L. Massera, Contributions to Stability Theory, The Annals of Mathematics, vol.64, issue.1, pp.182-206, 1956.
DOI : 10.2307/1969955

A. Saberi, P. V. Kokotovic, and H. J. Sussmann, Global Stabilization of Partially Linear Composite Systems, SIAM Journal on Control and Optimization, vol.28, issue.6, pp.1491-1503, 1990.
DOI : 10.1137/0328079

P. Sannuti and A. Saberi, Special coordinate basis for multivariable linear systems???finite and infinite zero structure, squaring down and decoupling, International Journal of Control, vol.45, issue.5, pp.1655-1704
DOI : 10.1109/TAC.1981.1102551

?. Ir, such that u(r)--0 one has LV(r):v(i@D -v(") and otherwise, g(r,z,u) being homogeneous of degree 2 with respect to u one gets: Lv(r):v(f (,)) -v(,) -ft-On"(')ll'+ ll, Global Stabilization of Nonaffine Control Systems It follows that

R. 4. If, in addition, / and V arc both C-functions, by choosing Kt and Kz C-, the stabilizing feedback law @.24) becomes also C-. In the next section, we turn our interest to the single-input case (*:1) for which we give more general sufrcient condition for stabilization

. Single-input-case-consid, er the continuous-time nonlinear system (4.2) with the control u ? lR, and 4. Global Stabilization of Nonaffine Control Systems 4.6 References lll Z.Artstein. Stabilization with relaxed controls. Nonli,near Anal, TMA, issue.7, pp.1163-1173, 1983.

R. W. Di and . Geometri, Asymptotic stability and feedback stabilization, c Control Theory, pp.181-191, 1983.

J. M. Coron, A necessary condition for feedback stabilization. Sgstems A Control Letters, pp.227-232, 1990.

J. M. Coron, Linearized Control Systems and Applications to Smooth Stabilization, SIAM Journal on Control and Optimization, vol.32, issue.2, pp.358-386, 1994.
DOI : 10.1137/S0363012992226867

J. P. Gauthier and G. Bornard, Outi,ls et modèIes mathémati,ques pour l'automati,que et la théori,e du si,gnal, chapter Stabilisation des systèmes non linéaires, pp.307-324, 1981.

V. Jurdjevic and J. P. Quinn, Controllability and stability, Journal of Differential Equations, vol.28, issue.3, pp.381-389, 1978.
DOI : 10.1016/0022-0396(78)90135-3

N. Kalouptsidis and J. Tsinias, Stability improvement of nonlinear systems by feedback, IEEE Transactions on Automatic Control, vol.29, issue.4, pp.36-467, 1984.
DOI : 10.1109/TAC.1984.1103518

M. A. Krasnosel-'ski and P. P. Zabreiko, Geometri,c Methods of nonli,near Analys'is, 1984.

J. P. Lasalle, The stabi.li,tg and control of di,scret processes, 1986.

J. P. Lasalle, S. Lefschetz, . Stabi, and . Li, apunou's direct method wi,th appli,cat'ions, 1961.

K. K. Lee and A. Araposthathis, Rema,rks on smooth feedback stabilization of nonlinear system Systems U Control Letters, p.4, 1988.

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

E. D. Sontag, A universal construction of a,rstein's theorem on nonlinear stabiliza' tion. ^ggrstems ?i Control Letters, pp.117-123, 1989.

E. D. Sontag, Feedback stabilization of nonlinea,r systemsRobust Control of Linear Sgstems and N onli,near C ontrol, pp.61-81, 1990.

J. Tsinias, Sufficient Lyaounov-like conditions for stabilizabibry. Mathemati,cs of control, Si,gnals and sgstems, pp.343-357, 1989.

P. Florchinger, A stochastic version of Jurdjevic???Quinn theorem, Stochastic Analysis and Applications, vol.12, issue.4, pp.473-480, 1994.
DOI : 10.1007/BF02551276

H. J. Kushner and S. Stability, Stabi,li,ty of Stochasti'c Dynam'ical Systems, Lecture Notes i'n Math, In R. Curtain éd, vol.294, pp.97297-97321

R. Outbib and G. Satlet, Stabilizability of the Angular velocity of a rigid body revisited, Systems ?i Control Letters, pp.93-98, 1992.

I. I02, Feedback Stabitization of Stochastic Nonlinear Composite Systems the soluti,onl rx :-0 of the stochasti,c di,fferenti,al equati,on (6.1 i,s sa'id to be asgmptoti'callg stable i,n probabi,li,ty. It i,s globallg asgmptoti,callg stable in probabi

. Then, 1 i,s stable (respecti .uely asymptoti,cally stable) i,n probabi,li'ty. It i's G.A.S.P i'f LV(r) (0, Vr?R', n+0 L04 6. Feedback Stabilization of Stochastic Nonlinear Composite Systems According to the decomposition of / given by (h3) and the one of g given by (6.7), one gets z.w(r,s) : (f @,0), VV(r) I -Trffioltna,0) + rt

. So, one has L.w(z) : (f @,0) VV(r) > -f,n'Qu +|r (n@,o)(s(", on'#Al) -; ( v, cr (H(u,a))' ffiaxnrr, o) * n@

P. V. Kokotovic and H. J. Sussmann, A positive real condition for global stabilization of nonlinear systems, Systems & Control Letters, vol.13, issue.2, pp.125-133, 1989.
DOI : 10.1016/0167-6911(89)90029-7

P. V. Kokotovic and H. J. Sussmann, The peaking Phenomenon and the global Stabilization of nonlinea"r systems, I.E.E.E Trans. Automat. Control, vol.36, issue.4, pp.424-440, 1991.

A. Saberi, P. V. Kokotovic, and H. J. Sussmann, Global stabilization of partially lineax composite systems, SIAM J. Control and Opti, issue.28, pp.1491-1503, 1990.

R. Chabour and P. Florchinger, Exponential mean square stability of partially linear stochastic systems, Applied Mathematics Letters, vol.6, issue.6, pp.91-95, 1993.
DOI : 10.1016/0893-9659(93)90085-2

L. Arnold and . Stochasti, ons : Theory and appli,cati,ons, L974)

H. J. Kushner, Stochastic stability Lecture Notes i,n Mathemati,cs, pp.97-121, 1972.