Realization by inspection

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