Stabilization of Impulsive Systems with Beyond-Interval Impulse Delays

This paper addresses the stabilization problem of linear impulsive systems with beyond-interval delays, for which state correlation exists between the current interval’s impulse state estimation and the historical feedback, making it difficult to obtain stability conditions for the system. In order to solve this problem, we develop a novel impulsive control method called interval partitioning, for which sufficient conditions for system stability are obtained. It indicates that time delays in impulses potentially contribute to the stabilization of linear systems with unstable system matrix, if there exist some historical state feedback. The effectiveness of the proposed approach is demonstrated through three examples.