Controllability of semilinear impulsive nonautonomous systems

Abstract

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.

Keywords:

• controllability
• nonlinear impulsive nonautonomous systems
• Rothe’s fixed-point theorem

2010 Mathematics Subject Classification:

• Primary 93B05
• Secondary 93C10.

Acknowledgements

This work has been supported by CDCHT-ULA-C-1796-12-05-AA and BCV.