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.
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.