Controllability for a class of time-varying controlled switching impulsive systems with time delays

This paper investigates two types of controllability for time-varying switching impulsive control systems with time delays and the relation between the two concepts. By characterizing the solution of the system, we establish necessary and sufficient conditions of the controllability of delayed switching impulsive systems with respect to a given switching time sequence. For some special cases, linear time-varying switching impulsive systems with or without time delay, the corresponding criteria are obtained. Compared with some existing results, the results presented here are more general and less conservative. Numerical examples are provided to show the effectiveness of the proposed methods.