A study of MBH-type realization algorithms

Realization algorithms, based on the reduction of a Markov-Block-Hankel (MBH) matrix, associated with the input/output description of a linear system, are considered as reduction algorithms on trivial realizations in block companion form. This approach allows for a very simple derivation of the basic solution, and for a geometrically transparent further development into various well-known algorithms (Ho and Kalman, 1965; Silverman, 1971; Rissanen, 1971), or algorithms introduced here. The relative quality of the (stable) orthonormal and (fast) pick-out procedures is compared, and within this class a new fast algorithm is described.

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