Abstract
We study the solutions to the delay differential equation equation ẋ(t) = -a(t)x(t - h), where the coefficient a(t) is not necessarily positive. It is proved that this equation is exponentially stable provided that a(t) = b + c(t) for some positive constant b less than π(2h), and the integral ∫0t c(s)ds is sufficiently small for all t > 0. In this case the 3/2-stability theorem is improved.
| Original language | English |
|---|---|
| Pages (from-to) | 1-5 |
| Number of pages | 5 |
| Journal | Electronic Journal of Differential Equations |
| Volume | 2010 |
| State | Published - 16 Aug 2010 |
Keywords
- Exponential stability
- Linear delay differential equation
ASJC Scopus subject areas
- Analysis