Eduardo D Sontag, Fabian Wirth
Remarks on universal nonsingular controls for discrete-time systems
The paper is published: Systems and Control Letters, 33(2):81-88,1998
93B03 Attainable sets
93B27 Geometric methods (including algebro-geometric)
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

Keywords: analytic systems, discrete time, forward accessibility, universal controls