 
Summary: Polyhedral Flows in Hybrid Automata y
Rajeev Alur 1z Sampath Kannan 1x Salvatore La Torre 2{
1 University of Pennsylvania
2 Universita degli Studi di Salerno
alur,kannan @cis.upenn.edu, slatorre @unisa.it
Abstract
A hybrid automaton is a mathematical model for hybrid systems, which combines, in a sin
gle formalism, automaton transitions for capturing discrete updates with dierential constraints for
capturing continuous
ows. Formal verication of hybrid automata relies on symbolic xpoint com
putation procedures that manipulate sets of states. These procedures can be implemented using
boolean combinations of linear constraints over system variables, equivalently, using polyhedra, for
the subclass of linear hybrid automata. In a linear hybrid automaton, the
ow at each control mode is
given by a rate polytope that constrains the allowed values of the rst derivatives. The key property
of such a
ow is that, given a stateset described by a polyhedron, the set of states that can be reached
as time elapses, is also a polyhedron. We call such a
ow a polyhedral
ow. In this paper, we study
if we can generalize the syntax of linear hybrid automata for describing
ows without sacricing the
polyhedral property. In particular, we consider
ows described by origindependent rate polytopes,
in which the allowed rates depend, not only on the current control mode, but also on the specic
state at which the mode was entered. We identify necessary and suÆcient conditions for a class of
ows described by origindependent rate polytopes to be polyhedral. We also propose and study
