Impulsive Stabilization of Linear Delay Differential Equations

The paper is concerned with stabilization of a scalar delay differention equation $$\dot{x}(t)-\sum _{k=1}^m{A}_k(t)x[h_k(t)]=0,t\ge 0,x(\xi )=\phi (\xi ),\xi <0,$$ by introducing impulses in certain moments of time $$x({\tau }_j)=B_{j}x({\tau }_j-0),j=1,2,\dots \mathrm{.}$$ Explicit stability results are presented both for the equation with positive coefficients and for the equation with $A_k$ being of arbitrary sign.