When the Poincare map associated with a periodic orbit of a hybrid dynamical system has constant-rank iterates; we demonstrate the existence of a constant-dimensional invariant subsystem near the orbit which attracts all nearby trajectories in finite time. This result shows that the long-term behavior of a hybrid model with a large number of degrees-of-freedom may be governed by a low-dimensional smooth dynamical system. The appearance of such simplified models enables the translation of analytical tools from smooth systems-such as Floquet theory-to the hybrid setting and provides a bridge between the efforts of biologists and engineers studying legged locomotion.
Title
Dimension Reduction Near Periodic Orbits of Hybrid Systems: Appendix
Published
2011-09-07
Full Collection Name
Electrical Engineering & Computer Sciences Technical Reports
Other Identifiers
EECS-2011-100
Type
Text
Extent
9 p
Archive
The Engineering Library
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