An Algorithm for Canonical Decomposition of a Linear Time-Invariant System
Hiroyuki Kajiwara, Katsuhisa Furuta · Transactions of the Society of Instrument and Control Engineers · 1982
This paper presents a numerically efficient algorithm to obtain Kalman's canonical decomposition for a linear time-invariant system. It is shown that eigen-vectors of a matrix QQ'PP', where P and Q' are the controllability matrix and observability matrix respectively, can be utilized to construct the state transformation matrix giving Kalman's canonical decomposition. The minimal realization of the system is easily obtained by the algorithm which means that the basis of the controllable and observable subspace are determined numerically.