Explicit exponential stability conditions for linear differential equations with several delays

New explicit conditions of exponential stability are obtained for the nonautonomous linear equation ˙x(t) + m k=1 ak(t)x hk(t) = 0, where m k=1 ak(t) 0,hk(t) t , by comparing this equation with a nonoscillatory exponentially stable equation of the form ˙x(t) + k∈I ak(t)x gk(t) = 0, where I ⊂ {1, . . . , m}, gk(t) t . Every comparison result gives 2m −1 different stability conditions due to the a priori choice of a subset I . © 2006 Elsevier Inc. All rights reserved