This book presents a modern and self-contained treatment of the Liapunov method for
stability analysis, in the framework of mathematical nonlinear control theory. A Particular
focus is on the problem of the existence of Liapunov functions (converse Liapunov ...

Abstract The goal of this article is to provide a construction of a homogeneous Lyapunov
function Image associated with a system of differential equations Image, under the
hypotheses:(1) Image vanishes at x= 0 and is homogeneous;(2) the zero solution of this ...

Abstract The exact boundary controllability of linear and nonlinear Korteweg-de Vries
equation on bounded domains with various boundary conditions is studied. When boundary
conditions bear on spatial derivatives up to order 2, the exact controllability result by ...

Dans cette thèse nous étudions plusieurs problèmes de stabilité/stabilisation à l'aide de la
théorie de Lyapunov. En premier lieu nous établissons qu'un système asymptotiquement
stable quasi homogène ― ou plus généralement présentant une symétrie ― possède une ...

Abstract. This paper is concerned with the internal stabilization of the generalized Korteweg–
de Vries equation on a bounded domain. The global well-posedness and the exponential
stability are investigated when the exponent in the nonlinear term ranges over the interval ...

Abstract. This paper is concerned with the controllability of the linear Korteweg–de Vries
equation on the domain Ω=(0,+∞), the control being applied at the left endpoint x= 0. It is
shown that the exact boundary controllability holds true in L2 (0,+∞) provided that the ...

Abstract The control of the surface of water in a long canal by means of a wavemaker is
investigated. The fluid motion is governed by the Korteweg-de Vries equation in lagrangian
coordinates. The null controllability of the elevation of the fluid surface is obtained thanks ...

Abstract The main result of this paper is a converse Liapunov theorem which applies to
systems of ordinary differential equations with a discontinuous righthand side. We treat both
the problem of local stability of an equilibrium position and the problem of boundedness of ...

Abstract The note deals with the state reconstruction of a class of discrete-time systems with
time-varying parameters. While usually, the parameters are assumed to be online available
and exactly known, the special and realistic situation when the parameters are known with ...