SIMULTANEOUS STABILIZABILITY OF 3 LINEAR-SYSTEMS IS RATIONALLY UNDECIDABLE

被引：84

作者：

BLONDEL, V ^{[1
]}

GEVERS, M ^{[1
]}

机构：

[1] UNIV CATHOLIQUE LOUVAIN,CESAME,B-1348 LOUVAIN,BELGIUM

来源：

MATHEMATICS OF CONTROL SIGNALS AND SYSTEMS | 1993年 / 6卷 / 02期

关键词：

SIMULTANEOUS STABILIZATION; DECIDABILITY; RATIONALLY DECIDABLE QUESTION;

D O I：

10.1007/BF01211744

中图分类号：

TP [自动化技术、计算机技术];

学科分类号：

0812 ;

摘要：

We show that the simultaneous stabilizability of three linear systems, that is the question of knowing whether three linear systems are simultaneously stabilizable, is rationally undecidable. By this we mean that it is not possible to find necessary and sufficient conditions for simultaneous stabilization of the three systems in terms of expressions involving the coefficients of the three systems and combinations of arithmetical operations (additions, subtractions, multiplications, and divisions), logical operations (''and'' and ''or''), and sign test operations (equal to, greater than, greater than or equal to,...).

引用

页码：135 / 145

页数：11

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