proper rational function

proper rational function

[′präp·ər ¦rash·ən·əl ‚fəŋk·shən]
(mathematics)
The quotient of a polynomial P by a polynomial Q whose order is greater than P.
McGraw-Hill Dictionary of Scientific & Technical Terms, 6E, Copyright © 2003 by The McGraw-Hill Companies, Inc.
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In this example, we consider a proper rational function in expanded form with ill-conditioned poles.
The set [R.sub.PS] means the ring of (Hurwitz) stable and proper rational functions. Then all transfer functions can be expressed by the ratio:
The following notation is used: [R.sub.ps] denotes the ring of Hurwitz-stable and proper rational functions and [I.sub.n] is the unit matrix of dimension n.

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