Some Transform Relations Between The Continuous-time Multivariable System Model and Its Sampled Version

The transform relations between the transfer function, given in the form of matrixing polynomial fraction, and its sampled version——pulse transfer function are investigated for linear time-invariantrnultivariable systems via state-space approach. The paper firstly presents the state-space models, whose parameter matrices are directly related to those in the transfer function matrices, both for the continuous-time and discrete-time rnultivariable systems, and then makes the state equations diagonalized. Secondly, the paper developes basic formulas for the discretization of the state-space model of continuous-time rnultivariable system, and furthermore, some basic relations used for the transformation of transfer function matrix into its sampled version.