Jochen Behrens, Fabian Wirth
A globalization procedure for locally stabilizing controllers
Preprint series: Berichte aus der Technomathematik 00-09, Universität Bremen
93B50 Synthesis problems
93C10 Nonlinear
For a nonlinear system with a singular point that is locally
asymptotically nullcontrollable we present a class of feedbacks that
globally asymptotically stabilizes the system on the domain of
asymptotic nullcontrollability.

The design procedure is twofold. In a neighborhood of the singular
point we use linearization arguments to construct a sampled (or
discrete) feedback that yields a feedback invariant neighborhood of
the singular point and locally exponentially stabilizes without the
need for vanishing sampling rate as the trajectory approaches the
equilibrium. On the remainder of the domain of controllability we
construct a piecewise constant patchy feedback that guarantees that
all Caratheodory solutions of the closed loop system reach the
previously constructed neighborhood.

Keywords: nonlinear system, feedback design, patchy feedback, control Lyapunov function