Stability Analysis for Impulsive Stochastic Time-Varying Systems
Xiaotai Wu, Wei Xing Zheng, Yang Tang, Xin Jin
Abstract
The average impulsive interval is widely used to describe the frequency of impulsive occurrence (FIO), where the occurrence number of impulses is bounded by a linear function of time interval length. However, the linear relationship may insufficiently or excessively characterize the occurrence number of impulses to stabilize impulsive time-varying systems. In this article, the impulsive density is introduced to describe a time-varying FIO, such that the occurrence number of impulses can be characterized more explicitly. Under the impulsive density, the asymptotical stability is considered for impulsive stochastic time-varying systems, where the continuous dynamics of systems, impulsive strengths, and instants are all assumed to be time-varying. In addition, the exponential stability is also investigated for impulsive stochastic time-varying systems with time-delay, which can extend some existing results. Two examples, including one example of the consensus for impulsive time-varying multiagent systems with time-delay, are presented to demonstrate the effectiveness of the proposed results.