State-space formulation of n-variable bilinear transformation for n-D systems

This paper establishes a general relationship between the state-space representations of an n-D continuous system and an n-D discrete system which are related by the n-variable bilinear transformation. In particular, a novel and simple formulation will be derived based on the theory of linear fractional transformation (LFT), by which the state-space representations of an n-D continuous system and an n-D discrete system can be directly calculated from each other such that they are related by the n-variable bilinear transformation. Moreover, it will be shown that the obtained formulation includes the existing results for the 1-D and 2-D cases as special cases. A numerical example is presented to illustrate the effectiveness of the proposed formulation.