Linear switching systems with slow growth of trajectories

被引：3

作者：

Protasov, Vladimir Yu ^{[1
,2
]}

机构：

[1] Moscow MV Lomonosov State Univ, Dept Mech & Math, Moscow, Russia

[2] Natl Res Univ, Higher Sch Econ, Fac Comp Sci, Moscow, Russia

来源：

SYSTEMS & CONTROL LETTERS | 2016年 / 90卷

关键词：

Dynamical systems; Linear switching systems; Growth of trajectories; Stability; Resonance; MARGINAL INSTABILITY; STABILITY; PRODUCTS;

D O I：

10.1016/j.sysconle.2016.01.006

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 prove the existence of positive linear switching systems (continuous time), whose trajectories grow to infinity, but slower than a given increasing function. This implies that, unlike the situation with linear ODE, the maximal growth of trajectories of linear systems may be arbitrarily slow. For systems generated by a finite set of matrices, this phenomenon is proved to be impossible in dimension 2, while in all bigger dimensions the sublinear growth may occur. The corresponding examples are provided and several open problems are formulated. (C) 2016 Elsevier B.V. All rights reserved.

引用

页码：54 / 60

页数：7

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