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)=-Σj=1mΣk=1^rijaijk(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.