Common eigenvector approach to exact order reduction for multidimensional Fornasini–Marchesini state-space models

Dongdong Zhao, Shi Yan, Shinya Matsushita and Li Xu

International Journal of Systems Science, 2019, vol. 50, issue 1, 60-74

Abstract: This paper proposes an exact order reduction approach for the multidimensional (n-D) Fornasini–Marchesini (F–M) model by making use of the common eigenvector. Specifically, by introducing the concept of common eigenvectors, sufficient conditions of exact order reductions are developed for an n-D F–M model, which are able to simultaneously deal with n eigenvalues of the system matrices $ A_1,\ldots , A_n $ A1,…,An of the n-D F–M model. The obtained results reveal, for the first time, the internal connection between the multiple eigenvalues of the system matrices and the reducibility of the considered n-D F–M model. Then, a corresponding algorithm is proposed to exactly reduce the order of an n-D F–M model as much as possible. Examples are given to illustrate the details as well as the effectiveness of the proposed approach.

Date: 2019
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DOI: 10.1080/00207721.2018.1543476

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