Improved noise‐to‐state stability criteria of random nonlinear systems with stochastic impulses

Abstract

This paper considers noise‐to‐state stability for random non‐linear systems with stochastic impulses. The impulsive random non‐linear systems contain three random characteristics: the second‐moment processes in continuous dynamics, the sequence of random variables in discrete dynamics, and the number of stochastic impulses obeyed a renewal process. Firstly, the improved criteria of noise‐to‐state stability are established for random non‐linear systems subject to unstable stochastic impulses based on the uniformly asymptotically stable function. Secondly, improved Lyapunov approaches of NSS with unstable stochastic continuous dynamics are accomplished by the uniformly exponentially stable function. Finally, two numerical examples are used to illustrate the feasibility of the proposed methods.

Stabilization of random nonlinear systems subject to deception attacks

“…The continuous dynamics in References 32,33 are all described by deterministic systems or stochastic differential equations. When , the criteria are similar to some results in References 25 and 29, but the random characteristic of impulsive intensity is different from those in References 25,29‐31.…”

“…Remark Although there are many results related to the stability of random impulsive nonlinear systems; see References 25,29‐33, they are all not suitable to investigate the stabilization problem for system (3). The continuous dynamics in References 32,33 are all described by deterministic systems or stochastic differential equations.…”