Stability conditions for linear nonautonomous delay differential equations

We derive new sufficient conditions for uniform asymptotic stability of the zero solution of linear non-autonomous delay differential equations. The equations considered include scalar equations of the form \[ x ′ ( t ) = − c ( t ) x ( t ) + ∑ i = 1 n b i ( t ) x ( t − T i ) x’ ( t ) = - c ( t )x ( t ) + ∑ i = 1^n {{b_i} ( t )x ( {t - {T_i}} )} \] where c ( t ) c ( t ) , b i ( t ) {b_i} ( t ) are continuous for t ≥ 0 t ≥ 0 and T i {T_i} is a positive number ( i = 1 , 2 , . . . , n ) (i = 1, 2,...,n) , and also systems of the form \[ x ′ ( <mml: