 
Summary: Sufficient Conditions for the Existence of Zeno Behavior in a Class of
Nonlinear Hybrid Systems via Constant Approximations
Aaron D. Ames, Alessandro Abate and Shankar Sastry
Abstract The existence of Zeno behavior in hybrid systems
is related to a certain type of equilibria, termed Zeno equilibria,
that are invariant under the discrete, but not the continuous,
dynamics of a hybrid system. In analogy to the standard
procedure of linearizing a vector field at an equilibrium point to
determine its stability, in this paper we study the local behavior
of a hybrid system near a Zeno equilibrium point by considering
the value of the vector field on each domain at this point, i.e., we
consider constant approximations of nonlinear hybrid systems.
By means of these constant approximations, we are able to
derive conditions that simultaneously imply both the existence
of Zeno behavior and the local exponential stability of a Zeno
equilibrium point. Moreover, since these conditions are in terms
of the value of the vector field on each domain at a point, they
are remarkably easy to verify.
I. INTRODUCTION
Zeno behavior occurs in a hybrid system if an infinite
