  We extend the definition of a Stochastic Hybrid Automaton (SHA) to overcome
limitations that make it difficult to use for on-line control. Since guard sets
do not specify the exact event causing a transition, we introduce a clock
structure (borrowed from timed automata), timer states, and guard functions
that disambiguate how transitions occur. In the modified SHA, we formally show
that every transition is associated with an explicit element of an underlying
event set. This also makes it possible to uniformly treat all events observed
on a sample path of a stochastic hybrid system and generalize the performance
sensitivity estimators derived through Infinitesimal Perturbation Analysis
(IPA). We eliminate the need for a case-by-case treatment of different event
types and provide a unified set of matrix IPA equations. We illustrate our
approach by revisiting an optimization problem for single node finite-capacity
stochastic flow systems to obtain performance sensitivity estimates in this new
setting.
