scholarly journals Exponential stability for a multi-particle system with piecewise interaction function and stochastic disturbance

2021 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Yipeng Chen ◽  
Yicheng Liu ◽  
Xiao Wang
Keyword(s):  
Exponential Stability ◽  
Particle System ◽  
Interaction Function ◽  
Stochastic Disturbance

String Exponential Stability With Mode Constraint of Stochastic Vehicle Following Systems

2013 ◽  
Vol 135 (6) ◽  
Author(s):  
Xiaohui Xu ◽  
Jiye Zhang ◽  
Lan Tang
Keyword(s):  
Exponential Stability ◽  
Sufficient Conditions ◽  
Original System ◽  
Analysis Method ◽  
Geometrical Analysis ◽  
Stochastic Disturbance ◽  
Infinite Dimensional ◽  
Vector Lyapunov Function ◽  
Lyapunov Function Method ◽  
The Stability

Associated with automatic vehicle following system is the problem of the stability of a platoon of vehicles. The stability with mode constraint is the property of damping disturbances as they travel away from the source in the system. In this paper, a class of infinite-dimensional vehicle longitudinal following system with stochastic disturbance is analyzed. By applying geometrical analysis method, a lemma for analyzing the stability of generalized vector comparison inequalities with respect to the original systems is established. With the help of the lemma, some sufficient conditions for assuring the string exponential stability with mode constraint of the original system are obtained by applying vector Lyapunov function method. The obtained conditions are less conservative than the existing ones. A numerical example is given to show the effectiveness of the established conditions.

scholarly journals Mean Square Exponential Stability of Stochastic Complex-Valued Neural Networks with Mixed Delays

Complexity ◽  
2019 ◽  
Vol 2019 ◽  
pp. 1-20 ◽  
Author(s):  
Xiaohui Xu ◽  
Jibin Yang ◽  
Yanhai Xu
Keyword(s):  
Neural Networks ◽  
Exponential Stability ◽  
Sufficient Conditions ◽  
Mixed Delays ◽  
Mean Square ◽  
Integral Theorem ◽  
Stochastic Disturbance ◽  
Mean Square Exponential Stability ◽  
The Mean ◽  
Complex Valued

This paper investigates the mean square exponential stability problem of a class of complex-valued neural networks with stochastic disturbance and mixed delays including both time-varying delays and continuously distributed delays. Under different assumption conditions concerning stochastic disturbance term from the existing ones, some sufficient conditions are derived for assuring the mean square exponential stability of the equilibrium point of the system based on the vector Lyapunov function method and Ito^ differential-integral theorem. The obtained results not only generalize the existing ones, but also reduce the conservatism of the previous stability results about complex-valued neural networks with stochastic disturbances. Two numerical examples with simulation results are given to verify the feasibility of the proposed results.

scholarly journals Robust Exponential Stability of Recurrent Neural Networks with Deviating Argument and Stochastic Disturbance

2020 ◽  
Vol 13 (4) ◽  
pp. 794-806
Author(s):  
Zha Mingxin ◽  
Si Wenxiao ◽  
Xie Tao
Keyword(s):  
Neural Networks ◽  
Exponential Stability ◽  
Recurrent Neural Networks ◽  
Robust Exponential Stability ◽  
Stochastic Disturbance ◽  
Deviating Argument ◽  
Know How ◽  
Exponentially Stable ◽  
The Stability ◽  
Upper Boundary

It is well known that deviating argument and stochastic disturbance may derail the stability of recurrent neural networks (RNNs). This paper discusses the robustness of global exponential stability (GES) of RNNs accompanied with deviating argument and stochastic disturbance. For a given global exponentially stable RNNs, it is interesting to know how much the length of the interval of piecewise function and the interference intensity so that the disturbed system may still be exponentially stable. The available upper boundary of the range of piecewise variables and the interference intensity in the disturbed RNNs to keep GES are the solutions of some transcendental equations. Finally, some examples are provided to demonstrate the efficacy of the inferential results.

Real-time meshless deformation based on particle system and shape matching

2009 ◽  
Vol 28 (12) ◽  
pp. 3007-3009
Author(s):  
Wang-gen WAN ◽  
Ji-cheng LIN ◽  
Xiao-qing YU ◽  
Huan DING ◽  
Xiao-hui TAN
Keyword(s):  
Real Time ◽  
Shape Matching ◽  
Particle System

A study on the fouling phenomena of a microfiltration membrane

2004 ◽  
Vol 4 (5-6) ◽  
pp. 223-231
Author(s):  
H.-H. Yeh ◽  
W.-H. Wang
Keyword(s):  
Salicylic Acid ◽  
Humic Acid ◽  
Calcium Ion ◽  
Colloidal Particles ◽  
Alginic Acid ◽  
Particle System ◽  
Feed Water ◽  
Permeate Flux ◽  
Widespread Application ◽  
Latex Beads

The utilization of membrane processes for drinking water treatment has become more popular. However, fouling by source water probably is the major factor prohibits its widespread application. In this research, the fouling phenomena of a microfiltration (MF) membrane were studied. The interactions among colloidal particles, calcium ion, and dissolved organics, such as salicylic acid, humic acid, and alginic acid, on MF fouling were focused. A lab-scale single hollow fiber MF membrane, made of polyvinylidenefluoride (PVDF), module was used. The results show that, for single organic compound, the extent of fouling caused by humic acid was higher that of alginic acid. For the latter, the permeate flux decrease at lower pH was more significant than those at higher pH. For low MW salicylic acid, both rejection and flux decrease were minor. It seems that solubility have strong correlation with fouling rate. The higher the solubility is, the lower the fouling rate. For sole colloidal particle system, latex beads with diameter close to the pore size of MF membrane showed severe fouling. Adding Ca can aggregate the latex beads, and alleviate fouling. However, calcium ion also found to increase fouling of alginic acid on membrane under neutral or alkali pH condition, probably via charge neutralization and/or bridging. In conclusion, MF fouling seems to be strongly related to the type of organics, size of colloidal particles, and the existence of divalent ions, in the feed water.

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