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Blowing Up Affine Hybrid Systems Aaron D. Ames* and Shankar Sastry*

Summary: Blowing Up Affine Hybrid Systems
Aaron D. Ames* and Shankar Sastry*
Department of EECS
University of California at Berkeley
Berkeley, CA 94720
Abstract-- In this paper we construct the "blow up" of an
affine hybrid system H, i.e., a new affine hybrid system Bl(H)
in which H is embedded, that does not exhibit Zeno behavior.
We show the existence of a bijection between periodic
orbits and equilibrium points of H and Bl(H) that preserves
stability; we refer to this property as P-stability equivalence.
If H is an affine hybrid system, we introduce its blow
up Bl(H) which is also an affine hybrid system. The
primary benefit of considering Bl(H) is that it is not
Zeno, although its structure suggests many other interesting
properties not generally found in affine hybrid systems. In
order to demonstrate that Bl(H) is in some way equivalent
to H, P-stability equivalence is introduced. If OH


Source: Ames, Aaron - Department of Mechanical Engineering, Texas A&M University


Collections: Engineering