Realization and canonicity for implicit systems. (English) Zbl 0666.93018
This paper studies realization theory and canonicity conditions for implicit systems. Here an implicit system is any system defined by an input-output finite-dimensional, linear, time-invariant relation in discrete or continuous time. The familiar definitions of canonicity and minimality are extended to such systems. A reduced form is used to prove the equivalence of minimality and canonicity. The notion of transfer function is replaced by that of an external form and it is shown that a minimal realization can always be achieved.
Reviewer: S.Campbell
MSC:
93B15 | Realizations from input-output data |
93B20 | Minimal systems representations |
34A99 | General theory for ordinary differential equations |
93B10 | Canonical structure |
93C05 | Linear systems in control theory |