01266nas a2200133   4500008004100000245012000041210006900161260002900230520070800259653001300967100001600980700001100996856012501007       2006                        eng d00aA converse Lyapunov theorem for semiglobal practical asymptotic stability and application to cascades-based control0 aconverse Lyapunov theorem for semiglobal practical asymptotic st  aSan Diego, USAcDecember3 a<p>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.</p>
10aRobotics1 aChaillet, A1 aLor, A  uhttp://118699.obes.asia/publications/converse-lyapunov-theorem-semiglobal-practical-asymptotic-stability-and-application