Reference:
B. De Schutter,
"Minimal state-space realization in linear system theory: An
overview," Journal of Computational and Applied Mathematics,
Special Issue on Numerical Analysis in the 20th Century - Vol. I:
Approximation Theory, vol. 121, no. 1-2, pp. 331-354, Sept. 2000.
Abstract:
We give a survey of the results in connection with the minimal state
space realization problem for linear time-invariant systems. We start
with a brief historical overview and a short introduction to linear
system theory. Next we present some of the basic algorithms for the
reduction of non-minimal state space realizations and for the minimal
state space realization of infinite or finite sequences of Markov
parameters of linear time-invariant systems. Finally we discuss some
extensions of this problem to other classes of systems and point out
some related problems.