Linear impulsive periodic system with time-varying generating operators on banach space

A class of the linear impulsive periodic system with time-varying generating operators on Banach space is considered. By constructing the impulsive evolution operator, the existence of T-0-periodic PC-mild solution for homogeneous linear impulsive periodic system with time-varying generating operators is reduced to the existence of fixed point for a suitable operator. Further the alternative results on T-0-periodic PC-mild solution for nonhomogeneous linear impulsive periodic system with time-varying generating operators are established and the relationship between the boundness of solution and the existence of T-0-periodic PC-mild solution is shown. The impulsive periodic motion controllers that are robust to parameter drift are designed for a given periodic motion. An example is given for demonstration.