Solution to the Generalized Champagne Problem on Simultaneous Stabilization of Linear Systems

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}.