Controllability of Nonlinear Impulsive and Switching Systems With Input Delay

In this article, the controllability is investigated for nonlinear impulsive and switching systems with input delay. Using the fixed point method, two controllability conditions are developed for such systems under different nonlinear constraints. First, the Lipschitz nonlinear condition is considered. A control mapping is constructed based on the input matrix condition, and a nonlinear operator is introduced to convert the controllability into the existence of a fixed point. A sufficient controllability criterion is obtained under the Banach’s contraction mapping principle. Second, a linear growth condition is imposed on the nonlinearity. A switched control mapping is constructed using the inverse of controllability matrix, and a corresponding nonlinear operator is introduced. An alternative controllability condition is then developed by resorting to the Rothe’s fixed point theorem. It is shown that the system controllability can be influenced by the impulsive and switching factors, beyond the delayed part and the nonlinearity. Two numerical examples are given to verify the theory.