We present a new representation for hybrid phase-portrait analysis, called the qualitative state/ parameter space, wherein a physical system’s dynamics are classified into discrete regions of qualitatively identical behavior. This classification is performed using automated phase-portrait analysis techniques and an abstraction scheme from the dynamical systems literature called cell dynamics. This hybrid representation is useful for input-output modeling of dynamical systems; among other things, it is a very natural way to reason about multiple sets of observations over a given system. Issues about the transitions between these discrete regions are analogous to many of the issues found in the hybrid systems literature. Our representation is an essential element of the input-output modeling component of the PRET automated system identification program.