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Resume Nous nous interessons a la stabilisation des systemes bilineaires homogenes. Nous donnons des conditions suffisantes pour qu'un systeme bilineaire soit stabilisable par « feedback a homogene de degre zero. Le feedback stabilisant est donne explicitement.

The aim of this paper is to study the feedback stabihzability of a class of control bilinear stochastic differential systems when control terms appear in both the drift and the noise coefficients. The method developped in this paper is based on the stochastic Lyapunov machinery and uses the stochastic version of Artstein’s theorem.

The purpose of this paper is to state sufficient conditions for the existence of linear feedback laws which render the equilibrium solution of a composite partially linear stochastic system (the linear part of which is deterministic) exponentially stable in mean square.

This paper gives a necessary and sufficient condition for the stabilization of planar bilinear systems. Local stabilization results are obtained for other systems.

In this paper, we give a class of nonlinear systems which cannot be stabilized by C1-feedback, but can be realized by homogeneous feedback of degree zero. The second part gives an observer and proves that the system is stabilized when, in the feedback, the state is replaced by the estimation given by the observer.

In this paper, we investigate the C1-stabilizability of affine control nonlinear systems in the plane. The feedback laws are given by means of Center manifold machinery.

This paper gives a necessary and sufficient condition for stabilization of planar bilinear systems. Local stabilization results are obtained for other systems.