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Summary: Almost global stabilization of the inverted
pendulum via continuous state feedback
David Angeli a
a Dip. Sistemi e Informatica,
Universita di Firenze,
Via di Santa Marta 3,
50139 Firenze, Italy
Abstract
Continuous state feedback laws are presented for \almost" global stabilization of
the planar inverted pendulum on a cart. The synthesis is carried out exploiting
energy-shaping techniques and a suitable smooth switching between positive and
negative feedback. Some of the employed ideas could be possibly generalized to the
problem of stabilization of systems with multiple equilibrium points.
Key words: Stability properties, Lyapunov methods, mechanical systems, energy
control, continuous control
1 Introduction
The project of control laws for underactuated mechanical systems often presents
a serious challenge for designers. This happens not only because of intrinsic
diĘculties related with the low number of actuators, but also because me-
chanical systems typically evolve on manifolds which are not di eomorphic
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