TY - JOUR
T1 - On Controllability, Observability, and Minimality of 2-D Separable Denominator Systems
T2 - A New Approach Based on the Reduced-Dimensional Decomposition
AU - Lin, Tao
AU - Kawamata, Masayuki
AU - Higuchi, Tatsuo
PY - 1987/8
Y1 - 1987/8
N2 - In this paper, controllability, observability, and minimality of 2-D separable denominator systems (SDS‘s) are studied based on the reduced-dimensional decomposition proposed by the authors in a previous paper. These notions of an SDS are completely related to those of its I-D decomposition pair. On the basis of these relations, several new necessary and sufficient conditions are given to examine these notions of an SDS. These conditions are much simpler than any conventional conditions. Moreover, using these relations, we prove that the basic system theoretical problems of constructing controllable (or observable) or minimal state-space realizations for a given 2-D separable denominator transfer function matrix can be changed into corresponding 1-D problems. Therefore, any techniques developed in 1-D system theory can be used to solve these 2-D problems.
AB - In this paper, controllability, observability, and minimality of 2-D separable denominator systems (SDS‘s) are studied based on the reduced-dimensional decomposition proposed by the authors in a previous paper. These notions of an SDS are completely related to those of its I-D decomposition pair. On the basis of these relations, several new necessary and sufficient conditions are given to examine these notions of an SDS. These conditions are much simpler than any conventional conditions. Moreover, using these relations, we prove that the basic system theoretical problems of constructing controllable (or observable) or minimal state-space realizations for a given 2-D separable denominator transfer function matrix can be changed into corresponding 1-D problems. Therefore, any techniques developed in 1-D system theory can be used to solve these 2-D problems.
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U2 - 10.1109/TCS.1987.1086219
DO - 10.1109/TCS.1987.1086219
M3 - Article
AN - SCOPUS:0023401672
VL - 34
SP - 962
EP - 967
JO - IEEE Transactions on Circuits and Systems
JF - IEEE Transactions on Circuits and Systems
SN - 0098-4094
IS - 8
ER -