The stability of saturated linear dynamical systems is undecidable

被引：29
|
作者：
Blondel, VD
Bournez, O
Koiran, P
Tsitsiklis, JN
机构：
[1] Catholic Univ Louvain, CESAME, Div Appl Math, B-1348 Louvain, Belgium
[2] LORIA, F-54602 Villers Les Nancy, France
[3] INRIA Lorraine, F-54602 Villers Les Nancy, France
[4] Ecole Normale Super Lyon, LIP, F-69364 Lyon 07, France
[5] MIT, LIDS, Cambridge, MA 02139 USA
来源：
JOURNAL OF COMPUTER AND SYSTEM SCIENCES | 2001年 / 62卷 / 03期
基金：
美国国家科学基金会;
关键词：
dynamical systems; saturated linear systems; piecewise affine systems; hybrid systems; mortality; stability; decidability;
D O I：
10.1006/jcss.2000.1737
中图分类号：
TP3 [计算技术、计算机技术];
学科分类号：
0812 ;
摘要：
We prove that several global properties (global convergence, global asymptotic stability, mortality, and nilpotence) of particular classes of discrete time dynamical systems are undecidable. Such results had been known only for point-to-point properties. We prove these properties undecidable for saturated linear dynamical systems, and for continuous piecewise affine dynamical systems in dimension 3. We also describe some consequences of our results on the possible dynamics of such systems. (C) 2001 Academic Press.
引用
收藏
页码：442 / 462
页数：21
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