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

Uniform exponential stability of linear systems with time varying coefficients x(i)(t) = -Sigma(m)(j=1)Sigma(rij)(k=1)a(ij)(k)(t)x(j)(h(ij)(k)(t)), i = 1,...,m is studied, where t >= 0; m and r(ij), i,j = 1,...,m are natural numbers, a(ij)(k) : [0,infinity) -> R and h(ij)(k) : [0,infinity) -> 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. (C) 2014 Elsevier Inc. All rights reserved.