2006/07/19 by Qiang Guan, Long Wang, Guan, Qiang +9
Mathematics · #37F10 #Dynamical Systems (math.DS) #FOS: Mathematics #math.DS #msc:37F10
paper · pdf · doi:10.48550/arxiv.math/0607445
arxiv created 2006/07/19 · arxiv updated 2009/12/01
The well-known "Generalized Champagne Problem" on simultaneous stabilization of linear systems is solved by using complex analysis \citeA73,C78,G69,N52,R87 and Blondel's technique \citeB94,BG93,BGMR94. We give a complete answer to the open problem proposed by Patel et al. \citeP99,PDV02, which automatically includes the solution to the original "Champagne Problem" \citeBG93,BGMR94,BSVW99,LKZ99,P99,PDV02. Based on the recent development in automated inequality-type theorem proving \citeY98,Y99,YHX01,YX05,YX03, a new stabilizing controller design method is established. Our numerical examples significantly improve the relevant results in the literature \citeLKZ99,PDV02.