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Formal and Practical Completion of Lagrangian Hybrid Systems Yizhar Or and Aaron D. Ames
 

Summary: Formal and Practical Completion of Lagrangian Hybrid Systems
Yizhar Or and Aaron D. Ames
Abstract-- This paper presents a method for completing
Lagrangian hybrid systems models in a formal manner. That
is, given a Lagrangian hybrid system, i.e., a hybrid system that
models a mechanical system undergoing impacts, we present
a systematic method in which to extend executions of this
system past Zeno points by adding an additional domain to
the hybrid model. Moreover, by utilizing results that provide
sufficient conditions for Zeno behavior and for stability of Zeno
equilibria in Lagrangian hybrid systems, we are able to give
explicit bounds on the error incurred through the practical
simulation of these completed hybrid system models. These
ideas are illustrated on a series of examples, and are shown
to be consistent with observed reality.
I. INTRODUCTION
The existence of Zeno behavior--an infinite number of
discrete transitions in a finite amount of time--is an in-
triguing phenomenon which is unique to hybrid systems.
When modeling real physical systems as hybrid systems, it

  

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

 

Collections: Engineering