Stability and asymptotically periodic solutions of hybrid systems with aftereffect

In this paper, we study hybrid linear systems of functional differential equations with aftereffect using the Azbelev $W$-method. Two model equations are considered and Banach spaces of right-hand sides and solutions, which are spaces of asymptotically periodic functions, are examined. Analogs of the Bohl–Perron theorem on the asymptotic stability and on the existence of limits of solutions are obtained.