Contents I. Introduction
Impulsive systems can be classified as hybrid systems, and incorporate both continuous-time and discrete-time dynamics [1], [2]. As a unique type of hybrid system, impulsive systems have found extensive applications in modeling real-world dynamic processes that demonstrate sudden changes occurring at discrete moments, see [3], [4], [5], and [6]. For example, networked control systems [7], [8], sampled-data control [9], [10], secure communication [11], [12], event-triggered synchronization problem [13], [14], [15], control problems of multi-agent systems [16], [17]. Depending on whether impulses have a positive effect on system stability, the study of impulsive system stability can be divided into two directions: impulsive control and impulse perturbation. The study of impulse perturbation typically centers around the robustness of systems with destabilizing impulses, see [18] and [19], whereas the study of impulsive control focuses on the case where impulses are used to control the continuous dynamics. Owing to the impulsive controller has the advantages of short operation time, low control cost and wide application range, it has attracted widespread attention, see [20] and [21].
