Stability of linear second-order time-varying differential equations via contractive polygons

被引：0
|
作者：
Taraba, Peter
Kitzing, Konrad [1 ]
Siegmund, Stefan [1 ]
机构：
[1] Tech Univ Dresden, Fac Math, Inst Anal, Dresden, Germany
来源：
SYSTEMS & CONTROL LETTERS | 2022年 / 162卷
关键词：
Second-order time-varying differential; equation; Exponential stability;
D O I：
10.1016/j.sysconle.2022.105186
中图分类号：
TP [自动化技术、计算机技术];
学科分类号：
0812 ;
摘要：
A damped harmonic oscillator x (t)+ a(1)x(t)+ a(0)x(t) = 0 with a(0), a(1) > 0 is known to be exponentially stable. We extend this result to time-varying positive coefficients a(0)(t), a(1)(t), t >= 0, which are bounded from above and below and satisfy supt & GE;0 a0(t) < (inf(t >= 0) a(1)(t))(2) and we thus further extend the sufficient condition sup(t >= 0) a(0)(t) <= 1/4(inf(t >= 0) a(1)(t))(2) by Levin (1969). Under slightly weaker assumptions we show uniform stability.(c) 2022 Elsevier B.V. All rights reserved.
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页数：6
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