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IMA Journal of Mathematical Control and Information 1993 10(4):323-344; doi:10.1093/imamci/10.4.323
© 1993 by Institute of Mathematics and its Applications
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Generalized state-space system matrix equivalents of a Rosenbrock system matrix

N. P. KARAMPETAKIS and A. I. VARDULAKIS

Department of Mathematics, Aristotle University of Thessaloniki Thessaloniki 54006, Greece

Bosgra & Van Der Weiden (1981) 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. Hayton et al. (1990) introduced the transformations of normal full system equivalence and full system equivalence. In the present work, we show that the Bosgra & 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.


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