For system identification of a continuous-time polynomial system, a subalgebraic identification procedure is defined. The procedure is motivated by the needs of system identification of the life sciences. The approach is inspired by the subspace identification algorithm which is adjusted to the subset of continuous-time polynomial systems. The procedure makes use of the subalgebraic procedure for system identification of a discrete-time polynomial system. An example illustrates the approach.

An algorithm is provided to reduce an unobservable rational system to an observable rational system while preserving its input-output behavior. The core of the algorithm lies in finding generators for the observation algebra generated by the unobservable rational system. Respective steps of the algorithm refer to standard operations in algebraic geometry. Examples are provided.