Minimal state-space realization in linear system theory: An overview (Q1587409)

The paper is a complete survey of the minimal state-space realization problem for linear time-invariant systems. After a brief historical overview and an introduction to the domain, the paper focusses on some of the basic algorithms as Rosenbrock's procedure of reduction of nonminimal realizations or algorithms for minimal state-space realizations of impulse responses based on the block Hankel matrices; Silverman's algorithm as well as the celebrated algorithm of B. L. Ho are presented. Different approaches to the minimal partial realization problem are examined, as well as minimal realization of noisy measurements of the impulse response or minimal realization based on step response data. Related problems and extensions are discussed like rational approximation, model reduction, identification, positive linear systems, max-puls-algebraic models or multidimensional systems. A bibliography containing 61 titles gives a full information about the discussed topic.