You are here : Control System Design  Index  Book Contents  Appendix C  Section C.8 C. Results from Analytic Function TheoryC.8.2 PoissonJensen Formula for the HalfPlane
Lemma C.1 Consider a function having the following properties
Consider also a point such that ; then
ProofLet
Then, is analytic within the closed unit disk. If we now apply Theorem C.9 to , we obtain
We also recall that, if is any complex number, then . Thus, the result follows upon equating real parts in the equation above and noting that
