Homogeneous Systems: Stability, Boundedness and Duality (original) (raw)
We introduce a duality principle for homogeneous vectorfields. As an application of this duality principle, stability and boundedness results for negative order homogeneous differential equations are obtained, starting from known results for positive order homogeneous differential equations. 1 Introduction Homogeneous vectorfields are vectorfields possessing a symmetry with respect to a family of dilations. They play a prominent role in various aspects of nonlinear control theory. See, for example, [1, 2, 5, 8] for some applications in feedback control. Recently, interesting results have been obtained for the particular class of positive order homogeneous differential equations: Peuteman and Aeyels [9] have proven that a timevarying positive order homogeneous differential equation is asymptotically stable if the associated averaged differential equation is asymptotically stable; Peuteman, Aeyels and Sepulchre [10] have proven that a time-varying positive order homogeneous differenti...
Related papers
On the Stability of Gradient-Like Systems
2014
This paper is dedicated to the study the problem of stability of some classes of gradient-like system of differential equations (both autonomous and non-autonomous cases). We present two main results. The first is a generalization of Absil & Kurdyka theorem about stability of gradient systems with analytic potential for non-gradient systems. Secondly we generalize for some classes of gradient-like non-autonomous systems the well-known Lagrange-Dirichet theorem.
Loading Preview
Sorry, preview is currently unavailable. You can download the paper by clicking the button above.