  The well-known "Generalized Champagne Problem" on simultaneous stabilization
of linear systems is solved by using complex analysis
\cite{A73,C78,G69,N52,R87} and Blondel's technique \cite{B94,BG93,BGMR94}. We
give a complete answer to the open problem proposed by Patel et al.
\cite{P99,PDV02}, which automatically includes the solution to the original
"Champagne Problem" \cite{BG93,BGMR94,BSVW99,LKZ99,P99,PDV02}. Based on the
recent development in automated inequality-type theorem proving
\cite{Y98,Y99,YHX01,YX05,YX03}, a new stabilizing controller design method is
established. Our numerical examples significantly improve the relevant results
in the literature \cite{LKZ99,PDV02}.
