| Abstract: | In this paper, the following problem is addressed: given a two-dimensional complete behavior\({\cal B}\) and one of its sub-behaviors\({\cal B}_B\), under what conditions a third complete behavior\({\cal B}_A\) can be found, such that\({\cal B} = {\cal B}_A + {\cal B}_B\) and\({\cal B}_A \cap {\cal B}_B\) is finite-dimensional autonomous? This constitutes a complete generalization of the decomposition theorem, as it represents a decomposition with “minimal intersection”, in which one of the two terms has been a priori fixed. The analysis carried on here completes the preliminary results reported in Bisiacco and Valcher, Multidimensional Systems and Signal Processing, vol. 13,2002, pp. 289–315]. and completely generalizes the direct sum decomposition problem presented in Bisiacco and Valcher, IEEE Transactions on Circuits and Systems Part I, CAS-I-48, no-4, 2001, pp. 490–494]. |
