| | |
Summary: Rank Properties of Poincaré Maps for Hybrid Systems with
Applications to Bipedal Walking
Eric D.B. Wendel
ericdbw@tamu.edu
Aaron D. Ames
aames@tamu.edu
Department of Mechanical Engineering
Texas A&M University
College Station, TX USA
ABSTRACT
The equivalence of the stability of periodic orbits with the
stability of fixed points of a PoincarŽe map is a well-known
fact for smooth dynamical systems. In particular, the eigen-
values of the linearization of a PoincarŽe map can be used to
determine the stability of periodic orbits. The main objec-
tive of this paper is to study the properties of PoincarŽe maps
for hybrid systems as they relate to the stability of hybrid
periodic orbits. The main result is that the properties of
PoincarŽe maps for hybrid systems are fundamentally differ-
ent from those for smooth systems, especially with respect
|
