Controllability of semilinear impulsive nonautonomous systems

In this paper we apply Rothe's type fixed-point theorem to prove the controllability of the following semilinear impulsive nonautonomous systems of differential equations [GRAPHICS] where [GRAPHICS] , [GRAPHICS] , A(t), B(t) are continuous matrices of dimension nxn and nxm, respectively, the control function u belongs to [GRAPHICS] and [GRAPHICS] , [GRAPHICS] , k = 1, 2, 3, horizontal ellipsis , p. Under additional conditions we prove the following statement: if the linear [GRAPHICS] is controllable on [0, tau], then the semilinear impulsive system is also controllable on [0, tau]. Moreover, we could exhibit a control steering the nonlinear system from an initial state z(0) to a final state z(1) at time tau > 0.