Complete Controllability of Piecewise Time-Varying Impulsive Systems with Multiple Input Delays

This paper deals with the complete controllability for piecewise linear time-varying impulsive systems with multiple time delays in input. The problem is addressed based on algebraic and geometric methods. First, an explicit solution for such systems is established via variation of parameters and mathematical induction. Then, based on the derived solution, complete controllability is investigated and several necessary and sufficient controllability criteria are established analytically for the underlying system. Finally, the obtained controllability conditions are verified through one numerical example. Compared with previous studies, the considered model is more general and the results obtained in this paper are less conservative.