Deciding stability and mortality of piecewise affine dynamical systems

被引：39

作者：

Blondel, VD

Bournez, O

Koiran, P

Papadimitriou, CH

Tsitsiklis, JN

机构：

[1] Univ Catholique Louvain, CESAME, B-1348 Louvain, Belgium

[2] LORIA, F-54506 Vandoeuvre Nancy, France

[3] Ecole Normale Super Lyon, LIP, F-69364 Lyon, France

[4] Univ Calif Berkeley, Dept Comp Sci, Berkeley, CA 94720 USA

[5] MIT, LIDS, Cambridge, MA 02139 USA

来源：

THEORETICAL COMPUTER SCIENCE | 2001年 / 255卷 / 1-2期

关键词：

discrete dynamical systems; piecewise affine systems; piecewise linear systems; hybrid systems; mortality; stability; decidability;

D O I：

10.1016/S0304-3975(00)00399-6

中图分类号：

TP301 [理论、方法];

学科分类号：

081202 ;

摘要：

In this paper we study problems such as: given a discrete time dynamical system of the form x(t + 1)= f(x(t)) where f: R-n --> R-n is a piecewise affine function, decide whether all trajectories converge to 0. We show in our main theorem that this Attractivity Problem is undecidable as soon as n greater than or equal to2. The same is true of two related problems: Stability (is the dynamical system globally asymptotically stable?) and Mortality (do all trajectories go through 0?). We then show that AM-activity and Stability become decidable in dimension 1 for continuous functions. (C) 2001 Elsevier Science B.V. All rights reserved.

引用

页码：687 / 696

页数：10

共 17 条

[1] THE ALGORITHMIC ANALYSIS OF HYBRID SYSTEMS [J].