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.

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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.