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 where , , A(t), B(t) are continuous matrices of dimension n×n and n×m, respectively, the control function u belongs to and , , k = 1, 2, 3, … , p.Under additional conditions we prove the following statement: if the linear is controllable on [0, τ], then the semilinear impulsive system is also controllable on [0, τ]. Moreover, we could exhibit a control steering the nonlinear system from an initial state z0 to a final state z1 at time τ > 0.