Input to state stability properties of nonlinear systems andapplications to bounded feedback stabilization using saturation

Abstract

The concepts of stability, attractivity and asymptotic stability for systems subject to restrictions of the input values are introduced and analyzed in terms of Lyapunov functions. A comparison with the well known input-to-state stability property introduced by Sontag is provided. We use these concepts in order to derive suficient conditions for global stabilization for triangular and feedforward systems by means of saturated bounded feedback controllers and also recover some recent results due to Teel. © 1997 Société de Mathématiques Appliquées et Industrielles.