Linear impulsive periodic system with time-varying generating operators on Banach space (Q2472260)

A class of linear impulsive periodic systems with time-varying generating operators on a Banach space is considered. By constructing an impulsive evolution operator, the existence of a \(T_0\)-periodic \(PC\)-mild solution for a homogeneous linear impulsive periodic system with time-varying generating operators is reduced to the existence of a fixed point for a suitable operator. Further alternative results on a \(T_0\)-periodic \(PC\)-mild solution for a nonhomogeneous linear impulsive periodic system with time-varying generating operators are established and the relationship between the boundedness of a solution and the existence of a \(T_0\)-periodic \(PC\)-mild solution is shown. Impulsive periodic motion controllers that are robust to the parameter drift are designed for a given periodic motion. An example is given for demonstration.