Stability of Nonlinear System With External Disturbance Under Multiple Cyber‐Attacks Via Delay‐Dependent Impulsive Control
Junfeng Guo, Fei Wang, Yunliang Wei, Chuan Zhang · Mathematical Methods in the Applied Sciences · 2025
ABSTRACT In this paper, the stochastically practically exponential stability (SPES) of nonlinear system with external disturbance under denial‐of‐service (DoS) attacks and deception attacks (DAs) is studied using delay‐dependent impulsive strategy. The main challenge of solving the concerned problem lies in the interplay among impulsive delay, external disturbance, DoS attacks and DAs. To overcome this challenge, a novel impulsive differential inequality is established at first. Then, by using the definitions of average impulsive delay (AID) and average impulsive interval (AII), sufficient conditions for realizing the SPES of the corresponding nonlinear system are derived, and a parametric upper bound on the state vector norm of the controlled system is obtained. Interestingly, our proposed results show that impulsive delay can reduce the negative impact of external disturbance and cyber‐attacks on stability of system. Finally, two numerical examples are presented to validate our theoretical findings.