Transformation of a continuous time-invariant linear system into a discrete one

Abstract

Abstract A discrete-time time-invariant linear system (DILS) is considered which has resulted from the discretization of a continuous-time time-invariant linear system (CILS) by the zero order hold. In this system, the system and input matrices are given by exp(AT) and $ where A and B are the system and input matrices of the CILS, and T is a sampling interval. Since they involve the matrix exponential, their computations are not easy. First, on the assumption that the Kalman canonical form of the CILS is sought, a formal Kalman canonical form of the DILS is determined. Second, with the use of this form and the decomposition of A into the projectors onto the generalized eigenspaces, an algorithm is presented which computes the system and input matrices of the DlLS.