Stochastic Finite-Time Stability for Stochastic Nonlinear Systems with Stochastic Impulses

Abstract

In this paper, some novel stochastic finite-time stability criteria for stochastic nonlinear systems with stochastic impulse effects are established. The results in this paper blackgeneralized the related results in from two aspects: 1. the model in is the deterministic systems, which means that the noise effect that can be described as a symmetric Markov process Brownian motion is considered in our models; 2. the stochastic finite-time stability criterion is established in this paper, not the asymptotic stability and the input-to-state stability that are studied in the form literature. Finally, an example is given to show the significance blackand usefulness of our results.

Exponential Stability for Second-Order Neutral Stochastic Systems Involving Impulses and State-Dependent Delay

“…Thus, the vital purpose of the present study is to bridge such a gap by making an attempt to deal with the second-order impulsive systems with stochastic effects and state-dependent delay. Comparing with [8,10,13,15,22,25,26], the results in this paper are new and original, as they have not considered the state-dependent delay.…”

“…It should be noted that the stability analysis of second-order systems with or without stochastic effects has been studied in [8,13,15]. Further, the stability of stochastic systems with impulses has been discussed in [10,22,25,26]. However, in practice, many second-order systems together with impulse effects are subjected to random loading.…”

“…The occurrence of the stochastic process in the mathematical model is unavoidable to characterize the physical structures. So, the stability analysis of stochastic nonlinear systems involving several effects was studied in [19][20][21][22][23][24]. Further, impulsive systems have been paid remarkable attention in various areas and many significant works have been attained by researchers.…”

Piecewise time-delay tri-stable stochastic resonance system and its application in bearing fault diagnosis

“…It can be seen that the outer ring signal is submerged completely in noise and the information at the characteristic frequency cannot be directly observed. Due to the strict limitations of the adiabatic approximation theory and linear response theory of stochastic resonance, the bearing fault signals must be converted to small parameter signals to process [34].The fault frequency of the outer ring signal is 107.2 Hz, which does not meet the adiabatic approximation theory, so a secondary sampling pre-processing of the fault signal is required, with the sampling frequency chosen as 12 kHz, and the secondary sampling [35] frequency is = f 5 Hz.…”

Probabilistic response determination of high-dimensional nonlinear dynamical systems enforced by parametric multiple Poisson white noises

“…However, compared to systems enforced by Gaussian white noise, much less attention has been paid to systems enforced by Poisson white noise (PWN). Nevertheless, systems enforced by PWN are prevalent in various fields, such as granular noise in physics (Hu 1994), chemical reactions in biochemistry (Winkelmann & Schütte 2020), population dynamics in ecological systems (Gardiner 2004), landatmosphere interaction in environmental science (Prahbu 1998), and stochastic dynamic loads on structures in civil engineering (Li & Chen 2009), etc. Dealing with PWN-driven systems involves challenges related to dealing with jump processes (i.e., path-discontinuous processes), computational costs in high-dimensional nonlinear scenarios, and the coupling between occurrence rates and system responses or states (i.e., parametric excitations) (Snyder 1975, Ibrahim 1985.…”