On the asymptotic behavior of solutions to a class of differential-difference equations

The forced delay differential equation
$$\dot x(t)=a(t)x(t-\omega),\ t\in\mathbb{R}_{+}$$
with complex coefficient $a(t)$ satisfying the condition $a(t+\omega)=Ma(t)$, $M\in\mathbb{C}$, is being considered. Effective sufficient conditions for asymptotic behaviour of solutions were obtained, in particular, the conditions for solutions' boundedness, convergence to some constant value and unboundedness.