Generalized state-space system matrix equivalents of a Rosenbrock system matrix

Bosgra & Van Der Weiden (1981) have given a procedure wherebya Rosenbrock system matrix may be reduced to an equivalent generalizedstate-space system matrix. The sense in which this is equivalentto the original system matrix is that the reduced system matrixexhibits identical system properties both at finite and infinitefrequencies. Hayton et al. (1990) introduced the transformationsof normal full system equivalence and full system equivalence.In the present work, we show that the Bosgra & Van Der Weidenreduction procedure is a full system-equivalence transformation,and a characterization of this equivalence in a matrix-transformationsense is also provided.