scholarly journals New criteria for exponential stability of linear neutral differential systems with distributed delays

Kybernetika ◽  
2021 ◽  
pp. 776-784
Author(s):  
Pham Huu Anh Ngoc ◽  
Thai Bao Tran ◽  
Nguyen Dinh Huy
Keyword(s):  
Exponential Stability ◽  
Distributed Delays ◽  
Differential Systems ◽  
New Criteria

scholarly journals Stochastically Globally Exponential Stability of Stochastic Impulsive Differential Systems with Discrete and Infinite Distributed Delays Based on Vector Lyapunov Function

Complexity ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-16
Author(s):  
Xiaoyan Liu ◽  
Quanxin Zhu
Keyword(s):  
Lyapunov Function ◽  
Exponential Stability ◽  
Distributed Delays ◽  
Differential Systems ◽  
Delay Term ◽  
Globally Exponential Stability ◽  
Impulsive Differential Systems ◽  
Vector Lyapunov Function ◽  
Infinite Distributed Delays ◽  
Impulsive Dynamics

This paper deals with stochastically globally exponential stability (SGES) for stochastic impulsive differential systems (SIDSs) with discrete delays (DDs) and infinite distributed delays (IDDs). By using vector Lyapunov function (VLF) and average dwell-time (ADT) condition, we investigate the unstable impulsive dynamics and stable impulsive dynamics of the suggested system, and some novel stability criteria are obtained for SIDSs with DDs and IDDs. Moreover, our results allow the discrete delay term to be coupled with the nondelay term, and the infinite distributed delay term to be coupled with the nondelay term. Finally, two examples are given to verify the effectiveness of our theories.

NEW CRITERIA ON GLOBAL EXPONENTIAL STABILITY OF BAM NEURAL NETWORKS WITH DISTRIBUTED DELAYS AND REACTION-DIFFUSION TERMS

2007 ◽  
Vol 17 (01) ◽  
pp. 43-52 ◽  
Author(s):  
XUYANG LOU ◽  
BAOTONG CUI
Keyword(s):  
Neural Networks ◽  
Exponential Stability ◽  
Global Exponential Stability ◽  
Reaction Diffusion ◽  
Kernel Functions ◽  
Distributed Delays ◽  
Analysis Technique ◽  
Inequality Technique ◽  
New Criteria ◽  
Theoretical Results

This paper presents new theoretical results on global exponential stability of bi-directional associative memory neural networks with distributed delays and reaction-diffusion terms based on the inequality technique, Lyapunov functional, and analysis technique. The results remove the usual assumption that the activation functions are of monotonous or differential character. Exponential converging velocity index is estimated, which depends on the delay kernel functions and system parameters. Finally, two numerical examples are given to show the validity and feasibility of our results.

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