English

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

Dynamical Systems 2022-06-14 v1

Abstract

Exponential stability of the second order linear delay differential equation in xx and uu-control x¨(t)+a1(t)x˙(h1(t))+a2(t)x(h2(t))+a3(t)u(h3(t))=0 \ddot{x}(t)+a_1(t)\dot{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)+b1(t)u(g1(t))+b2(t)x(g2(t))=0\dot{u}(t)+b_1(t)u(g_1(t))+b_2(t)x(g_2(t))=0 connects uu with the solution. Explicit sufficient conditions guarantee that both xx and uu decay exponentially.

Keywords

Cite

@article{arxiv.2206.05792,
  title  = {Exponential stability for a system of second and first order delay differential equations},
  author = {Leonid Berezansky and Elena Braverman},
  journal= {arXiv preprint arXiv:2206.05792},
  year   = {2022}
}

Comments

7 pages

R2 v1 2026-06-24T11:48:05.793Z