Exponential stability of systems of vector delay differential equations with applications to second order equations

Various results and techniques, such as the Bohl-Perron theorem, a priori estimates of solutions, M-matrices matrix measure, are applied to obtain new explicit exponential stability conditions for system vector functional differential equationsx˙i(t)=Ai(t)xi(hi(t))+∑j=1n∑k=1mijBijk(t)xj(hijk(t))+∑j=1n∫gij(t)tKij(t,s)xj(s)ds,i=1,…,n. Here xi unknown vector-functions, Ai,Bijk,Kij functions, hi,hijk,gij delayed arguments. Using these results, we deduce tests second order delay equations.