Papers by F.R. Wirth and E.D. Sontag

This paper shows that uniformly global asymptotic stability for a family of ordinary differential equations is equivalent to uniformly global exponential stability under a suitable nonlinear change of variables. The same is shown respectively for input-to-state stability, input-to-state exponential stability, and the property of finite square-norm gain ("nonlinear H-infty"). The results are shown for systems of any dimension not equal to 4 or 5.

For analytic discrete-time systems, it is shown that uniform forward accessibility implies the generic existence of universal nonsingular control sequences. A particular application is given by considering forward accessible systems on compact manifolds. For general systems, it is proved that the complement of the set of universal sequences of infinite length is of the first category. For classes of systems satisfying a descending chain condition, and in particular for systems defined by polynomial dynamics, forward accessibility implies uniform forward accessibility.