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

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

2006-07-19

arxiv.org/abs/math/0607445v1

Mathematics

Dynamical Systems

Scientific paper

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}.

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