STABILIZATION OF DISCRETE TIME SYSTEMS WITH A FOLD OR PERIOD DOUBLING CONTROL BIFURCATIONS

摘要

For nonlinear control systems with uncontrollable linearization around an equilibrium, the local asymptotic stability of the linear controllable directions can be easily achieved by linear feedback. Therefore we expect that the stabilizability of the whole system should depend on a reduced order model whose stabilizability depends on the linearly uncontrollable directions. The controlled center dynamics technique, introduced by the authors in a previous article, formalizes this intuition. In this paper we apply this approach to stabilize discrete-time systems with a fold or period-doubling control bifurcations.