Solution to the Generalized Champagne Problem on simultaneous stabilization of linear systems

Abstract

Abstract:The well-known "Generalized Champagne Problem" on simultaneous stabilization of linear systems is solved by using complex analysis [1,11,13,18,22] and Blondel's technique [5,6,8].We give a complete answer to the open problem proposed by Patel et al. [20,21], which automatically includes the solution to the original "Champagne Problem" [6,8,9,17,20,21]. Based on the recent development in automated inequality-type theorem proving [31,32,33,35,36], a new stabilizing controller design method is established. Our numerical examples significantly improve the relevant results in the literature [17,21].

Real solution number of the nonlinear equations in the SHEPWM technology

“…Based on these algorithms, a generic program called Discoverer [13] and a generic program called Bottema [14] were implemented as Maple packages. These latest achievements of mechanical proving have been widely used in various research areas, for example, Wei et al [15] established an easily testable necessary and sufficient algebraic criteria for delayindependent stability of a class of neutral differential systems by using the Complete Discrimination System for polynomials; He [16][17] and Guan [18] et al have given a series results of two open problems associated with simultaneous stabilization of linear systems, namely, French champagne problem and Belgian chocolate problem; Gao et al [19] used Wu-Ritt's zero decomposition algorithm [20] to give a complete triangular decomposition for the Perspective-ThreePoint (P3P) equation system. This decomposition provides the first complete analytical solution to the P3P problem and also gives a complete solution classification for the P3P equation system.…”

Some remarks on simultaneous stabilization problems of linear systems

“…(Simultaneous Stabilization) [1,10] [1, 10] k p 1 , p 2 , · · · , p k , c, c p i (i = 1, · · · , k) [1,6,10] , [1,2,4,5,[7][8][9] …”