id: 03858933
dt: j
an: 03858933
au: Nolte, Cornelia
ti: Generalized rank conditions for systems in a category.
so: Quaest. Math. 6, 211-226 (1983).
py: 1983
pu: NISC (National Inquiry Services Centre), Grahamstown; Taylor \& Francis,
    Abingdon
la: EN
cc: 
ut: Discrete-time bilinear systems; categorial framework; duality principle;
    reachability
ci: 
li: doi:10.1080/16073606.1983.9632301
ab: Discrete-time bilinear systems over an arbitrary commutative ring R with
    unity are given by the following equations: $$
    q(t+1)=Aq(t)+N(q(t))\otimes u(t)+Bu(t),y(t)=Cq(t) $$ with Q,Y and U R-
    modules and $N: Q\otimes U\to Q$, A: $Q\to Q$, $B: U\to Q$ and $C: Q\to
    Y$ R-homomorphisms. In the present paper those systems are considered
    as systems in the category R-Mod. The concepts of reachability and
    observability are defined and the known rank criteria for reachability
    of linear resp. bilinear systems are generalized for arbitrary systems
    in the category R- Mod with a state modul of finite height. Finally, in
    the categorial framework a general duality principle between
    reachability and observability of bilinear systems is established.
rv: D.Prätzel-Wolters