Stability of the Second Order Delay Differential Equations with a Damping Term

TL;DR

This paper derives explicit exponential stability conditions for second order delay differential equations with damping terms, enhancing understanding of their stability behavior under various delay and coefficient conditions.

Contribution

It provides new explicit stability criteria for complex second order delay differential equations with damping, extending existing theoretical results.

Findings

Explicit exponential stability conditions derived

Applicable to equations with multiple delays and damping terms

Enhances theoretical understanding of stability in delay differential equations

Abstract

For the delay differential equations $$ \ddot{x}(t) +a(t)\dot{x}(g(t))+b(t)x(h(t))=0, g(t)\leq t, h(t)\leq t, $$ and $$ \ddot{x}(t) +a(t)\dot{x}(t)+b(t)x(t)+a_1(t)\dot{x}(g(t))+b_1(t)x(h(t))=0 $$ explicit exponential stability conditions are obtained.