zbMATH — the first resource for mathematics

Generalized state-space system matrix equivalents of a Rosenbrock system matrix. (English) Zbl 0807.93009
Summary: G. H. Bosgra, and A. J. J. van der Weiden [Int. J. Control 33, 393-411 (1981; Zbl 0464.93021)] have given a procedure whereby a Rosenbrock system matrix may be reduced to an equivalent generalized state-space system matrix. The sense in which this is equivalent to the original system matrix is that the reduced system matrix exhibits identical system properties both at finite and infinite frequencies [G. E. Hayton, A. B. Walker and A. C. Pugh [Int. J. Control 52, No. 1, 1-14 (1990; Zbl 0702.93021)] introduced the transformations of normal full system equivalence. We show that the Bosgra and Van der Weiden reduction procedure is a full system-equivalence transformation, and a characterization of this equivalence in a matrix-transformation sense is also provided.

93B17 Transformations
93B10 Canonical structure
Full Text: DOI