Stabilization of Discrete Time Systems with a Fold or Period Doubling Control Bifurcation
| Authors: | Hamzi Boumediene, UCDavis, United States
Kang Wei, Naval Postgraduate School, United States
Krener Arthur J., UCDavis, United States |
|---|
| Topic: | 2.3 Non-Linear Control Systems |
|---|
| Session: | Nonlinear Stabilization II |
|---|
| Keywords: | Controlled Center Dynamics, Discrete-Time, FoldControl Bifurcation, Period-Doubling Control Bifurcation, Stabilization, Bird Foot Bifurcationfor Maps. |
|---|
Abstract
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.
