TY - CONF T1 - A converse Lyapunov theorem for semiglobal practical asymptotic stability and application to cascades-based control T2 - Proc. IEEE Int. Conf. on Decision and Control Y1 - 2006 A1 - A. Chaillet A1 - A. Lor KW - Robotics AB -

We present a converse Lyapunov result for nonlinear time-varying systems that are uniformly semiglobally asymptotically stable. This stability property pertains to the case when the size of initial conditions may be arbitrarily enlarged and the solutions of the system converge, in a stable way, to a closed ball that may be arbitrarily diminished by tuning a design parameter of the system (typically but not exclusively, a control gain). This result is notably useful in cascaded-based control when uniform practical asymptotic stability is established without a Lyapunov function, , ıt e.g.} via averaging. We provide a concrete example by solving the stabilization problem of a hovercraft.

JF - Proc. IEEE Int. Conf. on Decision and Control CY - San Diego, USA ER -