Symmetric Analysis of Stability Criteria for Nonlinear Systems with Multi-Delayed Periodic Impulses: Intensity Periodicity and Averaged Delay

This paper investigates the pth moment exponential stability of random impulsive delayed nonlinear systems (RIDNS) with multiple periodic delayed impulses. Moreover, the continuous dynamics are described by random delay differential equations whose random disturbances are driven by second-order moment processes. Using the periodic impulsive intensity (PII), average delay time (ADT), average impulsive delay (AID), as well as the Lyapunov method, we present some pth exponential stability criteria for impulsive random delayed nonlinear systems with multiple delayed impulses. Furthermore, the criterion is unified, which is not only applicable to stable or unstable original systems but also takes into account the coexistence of stabilizing and destabilizing impulses. The periodic structure of impulses and their intensities introduces an intrinsic temporal symmetry, which plays a critical role in determining the stability behavior of the system. This symmetry-based perspective highlights the fundamental impact of regularly recurring impulsive actions on system dynamics. Several illustrated examples are given to verify the effectiveness of our results.