Minimal state-space realization in linear system theory: an overview

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 nonminimal 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.