On the stabilizability of homogeneous systems of odd degree
We construct explicitly an homogeneous feedback for a class of single input, two dimensional and homogeneous systems.
On The Stabilizability of Homogeneous Systems Of Odd Degree
We construct explicitly an homogeneous feedback for a class of single input, two dimensional and homogeneous systems.
On the stabilizability of some classes of bilinear systems in
In this paper, we consider some classes of bilinear systems. We give sufficient condition for the asymptotic stabilization by using a positive and a negative feedbacks.
Separation principle for nonlinear systems: a bilinear approach
In this paper we investigate the local stabilizability of single-input nonlinear affine systems by means of an estimated state feedback law given by a bilinear observer. The associated bilinear approximating system is assumed to be observable for any input and stabilizable by a homogeneous feedback law of degree zero. Furthermore, we discuss the case of planar systems which admit bad inputs (i.e. the ones that make bilinear systems unobservable). A separation principle for such systems is given.
Only a level set of a control Lyapunov function for homogeneous systems
In this paper, we generalize Artstein’s theorem and we derive sufficient conditions for stabilization of single-input homogeneous systems by means of an homogeneous feedback law and we treat an application for a bilinear system.
Separation principle for nonlinear systems using a bilinear approximation
In this paper, we study the local stabilization problem of a class of planar nonlinear systems by means of an estimated state feedback law. Our approach is to use a bilinear approximation to establish a separation principle.
Stabilization of homogeneous polynomial systems in the plane
In this paper, we study the problem of stabilization via homogeneous feedback of single-input homogeneous polynomial systems in the plane. We give a complete classification of systems for which there exists a homogeneous stabilizing feedback that is smooth on and preserve the homogeneity of the closed loop system. Our results are essentially based on Theorem of Hahn in which the author gives necessary and sufficient conditions of stability of homogeneous systems in the plane.
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