A general state-space representation of n-variable bilinear transformation

Authors:
Shi Yan;Natsuko Shiratori;Hsin-Jang Shieh;Li Xu
Affiliations:
Department of Electronics and Information Systems, Akita Prefectural University, Akita, Japan;Department of Electronics and Information Systems, Akita Prefectural University, Akita, Japan;Department of Electrical Engineering, National Dong Hwa University, Hualien, Taiwan;Department of Electronics and Information Systems, Akita Prefectural University, Akita, Japan
Venue:
Signal Processing
Year:
2011

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Abstract

This paper proposes a general formulation of the relationship between the state-space representations of a multidimensional (n-D) continuous system and an n-D discrete system which are related by the n-variable bilinear transformation such that the state-space representations of these two related systems can be directly calculated from each other. The new formulation is derived based on the theory of linear fractional transformation (LFT) and the resultant form is simple and concise. Moreover, the relations among the proposed formulation and the existing 1-D and 2-D results are investigated and it turns out that the new formulation includes these existing results as special cases. A numerical example is presented to illustrate the effectiveness of the proposed formulation.