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Summary: IEEE TRANSACTIONS ON AUTOMATIC CONTROL, VOL. 41, NO. 4, APRIL 1996 589
Bilinear Transformation and Generalized
Singular Perturbation Model Reduction
B. Clapperton, F. Crusca, and M. Aldeen
Abstract-A new general bilinear relationshipis found between contin-
uous and discretegeneralized singular perturbation (GSP) reduced-order
models. This result is applied to the problem of derivingdiscreteanalogs
of continuoussingular perturbation and direct truncation model reduc-
tion and leads to a new definition of discrete"Nyquist" model reduction.
Also, "unit circle" bilinear transformations are used to relate several
known factsabout continuousand discretebalancedmodel reductionand
incorporate them into a symmetrical,unified framework.
I. INTRODUCTION
Model reduction may be achieved by a two-step process: 1)
identification of a dominant and a nondominant subsystem of the
high-order system and 2) elimination of the nondominant subsystem.
The identification step may be performed using methods such as
modal techniques [3], cost decomposition [18], matching of Markov
parameters [20], or balancing [151. For continuous-time systems, the
elimination step may be carried out by either the singular perturbation
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