Simple uniform exponential stability conditions for a system of linear delay differential equations

Abstract

Uniform exponential stability of linear systems with time varying coefficientsẋi(t)=-∑j=1m∑k=1rijaijk(t)xj(hijk(t)),i=1,…,mis studied, where t⩾0,m and rij,i,j=1,…,m are natural numbers, aijk:[0,∞)→R and hijk:[0,∞)→R are measurable functions. New explicit result is derived with the proof based on Bohl–Perron theorem. The resulting criterion has advantages over some previous ones in that, e.g., it involves no M-matrix to establish stability. Several useful and easily verifiable corollaries are deduced and examples are provided to demonstrate the advantage of the stability result over known results.