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

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 sufficient 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.