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 is in particular suitable for situations in which some of the coefficients are symbolic rather than numerical.

Minimal systems representations (msc 93B20), Canonical structure (msc 93B10), Linear systems (msc 93C05)
CWI
Department of Operations Research, Statistics, and System Theory [BS]

Rosenthal, J, & Schumacher, J.M. (1995). Realization by inspection. Department of Operations Research, Statistics, and System Theory [BS]. CWI.