Solution to the “Champagne problem” on the simultaneous stabilisation of three plants

Patel, Vijay V.

doi:10.1016/s0167-6911(99)00023-7

Cited by 13 publications

(29 citation statements)

References 5 publications

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“…Obviously, any element in U (cl(D)) and its inverse are analytic on cl(D). The following problem is the well-known "Champagne Problem" [6,8,9,17,20,21] of simultaneous stabilization. It illustrates the difficulty in the simultaneous stabilization of three systems in general.…”

Section: Solution To the Generalized Champagne Problemmentioning

confidence: 99%

“…Champagne Problem [6,8,9,17,20,21] Does there exist a controller that simultaneous 1 Note that, some researchers use the concept of Schur polynomials for polynomials with all roots lying inside unit circle. Most papers on simultaneous stabilization adopt the definition used in this paper, which makes it easier to use the results in complex analysis.…”

Section: Solution To the Generalized Champagne Problemmentioning

confidence: 99%

“…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.…”

Section: Introductionmentioning

confidence: 99%

“…However, by studying these specific problems, we can develop new tools and new methods for general simultaneous stabilization problem. As a matter of fact, by studying some specific systems, Blondel et al revealed the inherent relationship [5,6,8,20] between the simultaneous stabilization problem and complex analysis theory [1,11,13,18,22], and derived the deep theoretic results of rational undecidability for three systems [5,6].…”

Section: Introductionmentioning

confidence: 99%

“…

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.

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confidence: 99%

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

et al. 2007

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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].

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Section: Solution To the Generalized Champagne Problemmentioning

confidence: 99%

Section: Solution To the Generalized Champagne Problemmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

“…

…”

mentioning

confidence: 99%

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

et al. 2007

View full text Add to dashboard Cite

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].

show abstract