REALIZATION BY INSPECTION

We investigate which first-order representations can be obtained from high-order representations of linear systems ''by inspection,'' that i s, just by rearrangement of the data. Under quite weak conditions it i s possible to obtain minimal realizations in the so-called pencil form ; under stronger conditions one can obtain minimal realizations in sta ndard state-space form by inspection. The development is based on a re formulation of the realization problem as a problem of finding a compl ete set of basis vectors for the nullspace of a given constant matrix. Since no numerical computation is needed, the realization method in p articular is suitable for situations in which some of the coefficients are symbolic rather than numerical.