Affiliation:
1. Dep. Matemáticas, Univ. León , León , Spain
Abstract
Abstract
The regulator problem is solvable for a linear dynamical system
Σ
\Sigma
if and only if
Σ
\Sigma
is both pole assignable and state estimable. In this case,
Σ
\Sigma
is a canonical system (i.e., reachable and observable). When the ring
R
R
is a field or a Noetherian total ring of fractions the converse is true. Commutative rings which have the property that the regulator problem is solvable for every canonical system (RP-rings) are characterized as the class of rings where every observable system is state estimable (SE-rings), and this class is shown to be equal to the class of rings where every reachable system is pole-assignable (PA-rings) and the dual of a canonical system is also canonical (DP-rings).
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