Exponential stability for a system of second and first order delay differential equations

Leonid Berezansky; Elena Braverman

doi:10.1016/j.aml.2022.108127

paper

Exponential stability for a system of second and first order delay differential equations

arXiv:2206.05792 · doi:10.1016/j.aml.2022.108127

Abstract

Exponential stability of the second order linear delay differential equation in $x$ and $u$ -control $x ¨ (t) + a_{1} (t) x ˙ (h_{1} (t)) + a_{2} (t) x (h_{2} (t)) + a_{3} (t) u (h_{3} (t)) = 0$ is studied, where indirect feedback control $u ˙ (t) + b_{1} (t) u (g_{1} (t)) + b_{2} (t) x (g_{2} (t)) = 0$ connects $u$ with the solution. Explicit sufficient conditions guarantee that both $x$ and $u$ decay exponentially.

7 pages

References in corpus (1)

Stability and oscillation of linear delay differential equations