Exponential stability of singularly perturbed impulsive delay differential equations (Q864631)

The system of delay differential equations with impulses \[ \varepsilon \dot{x}(t)=A(t)x(t)+f(t,x(t-\tau(t))),\;t\geq t_0,\; t\neq t_k, \] \[ x(t)=\Phi(t),\; t\leq t_0,\; \qquad x(t_k)=J(t_k,x(t_k-)),\; k=1,2,\dots \] is considered. Criteria of exponential stability are established for sufficiently small \(\varepsilon >0.\)