New Stability Conditions for Linear Differential Equations with Several Delays

TL;DR

This paper introduces new explicit stability conditions for scalar nonautonomous linear delay differential equations with multiple measurable delays, enhancing the understanding of their asymptotic and exponential stability.

Contribution

The paper provides novel explicit stability criteria for equations with multiple delays, extending existing tests to more general measurable delay and coefficient functions.

Findings

New explicit stability conditions derived

Conditions applicable to equations with measurable delays

Comparison with existing stability tests included

Abstract

New explicit conditions of asymptotic and exponential stability are obtained for the scalar nonautonomous linear delay differential equation $$ \dot{x}(t)+\sum_{k=1}^m a_k(t)x(h_k(t))=0 $$ with measurable delays and coefficients. These results are compared to known stability tests.