You are here : Control System Design  Index  Book Contents  Appendix C  Section C.9 C. Results from Analytic Function TheoryC.9 Application of the PoissonJensen Formula to Certain Rational FunctionsConsider the biproper rational function given by
is a integer number, and and are polynomials of degrees and , respectively. Then, due to the biproperness of , we have that . Further assume that
Define
where and are polynomials. Then it follows that
We then have the following result
Lemma C.3 Consider the function defined in (C.9.2) and a point such that ; then
where is the Poisson kernel defined in (C.8.18).
ProofThis follows from a straightforward application of Lemma C.2.
