2-D partial fraction expansions and minimal commutative realizations

摘要

An analysis is presented of the class of rational functions in two variables realized by two-dimensional state-space models satisfying the commutativity assumption A/sub 1/A/sub 2/=A/sub 2/A/sub 1/. A complete characterization of these transfer functions is given in terms of the existence of a suitable partial fraction expansion. It is shown that, under the commutativity assumption, minimal realizations are unique modulo algebraic equivalence, and the minimality is equivalent to local observability and reachability.