Observation spaces for implicit input-output systems

The authors develop an algorithm which, given an input-output differential equation, produces a parameterization of the observation space of the underlying state space system. They extend previous results to a more general setting, so that the state space systems, in which the controls enter nonlinearly, can be accommodated, and, more importantly, deal with implicitly defined systems at both the input-output and state space level. Work by M. Flies and H. Hasler (1988) has demonstrated the importance of implicit input-output models, which yield only local state space descriptions. The results here are also important in understanding the realization problem