  It is rigorously proved that quasilinear impulsive systems possess
unpredictable solutions when a perturbation generated by an unpredictable
sequence is applied. The existence, uniqueness, as well as asymptotic stability
of such solutions are demonstrated. The system under consideration is with
regular moments of impulses, and for that reason a novel definition for
unpredictable functions with regular discontinuity moments is provided. To show
the existence of an unpredictable solution a Gronwall type inequality for
piecewise continuous functions is utilized. The theoretical results are
supported with an illustrative example.

Dynamical Systems;Chaotic Dynamics