Globally exponential stability of periodic solutions for nonlinear impulsive delay systems

2007 ◽  
Vol 67 (6) ◽  
pp. 1938-1946 ◽  
Author(s):  
Aizhi Weng ◽  
Jitao Sun
Keyword(s):  
Exponential Stability ◽  
Periodic Solutions ◽  
Delay Systems ◽  
Globally Exponential Stability ◽  
Impulsive Delay

Global exponential stability analysis of anti-periodic solutions of discontinuous bidirectional associative memory (BAM) neural networks with time-varying delays

2020 ◽  
Vol 21 (7-8) ◽  
pp. 807-820
Author(s):  
Xiangying Fu ◽  
Fanchao Kong
Keyword(s):  
Neural Networks ◽  
Exponential Stability ◽  
Periodic Solutions ◽  
Associative Memory ◽  
Time Varying ◽  
Bam Neural Networks ◽  
Bidirectional Associative Memory ◽  
Globally Exponential Stability ◽  
Discontinuous Activations ◽  
Neural Network System

AbstractThis paper is concerned with a class of bidirectional associative memory (BAM) neural networks with discontinuous activations and time-varying delays. Under the basic framework of differential inclusions theory, the existence result of solutions in sense of Filippov solution is firstly established by using the fundamental solution matrix of coefficients and inequality analysis technique. Also, the boundness of the solutions can be estimated. Secondly, based on the non-smooth Lyapunov-like approach and by construsting suitable Lyapunov–Krasovskii functionals, some new sufficient criteria are given to ascertain the globally exponential stability of the anti-periodic solutions for the proposed neural network system. Furthermore, we have collated our effort with some previous existing ones in the literatures and showed that it can take more advantages. Finally, two examples with numerical simulations are exploited to illustrate the correctness.

Razumikhin-type theorems on exponential stability of impulsive delay systems

2006 ◽  
Vol 71 (1) ◽  
pp. 47-61 ◽  
Author(s):  
Bin Liu ◽  
Xinzhi Liu ◽  
Kok Lay Teo ◽  
Qing Wang
Keyword(s):  
Exponential Stability ◽  
Delay Systems ◽  
Impulsive Delay

scholarly journals Existence and Stability of Periodic Solutions for Impulsive Fuzzy Cohen-Grossberg Neural Networks on Time Scales

2015 ◽  
Vol 0 (0) ◽  
Author(s):  
Qianhong Zhang ◽  
Jingzhong Liu ◽  
Yuanfu Shao
Keyword(s):  
Neural Networks ◽  
Exponential Stability ◽  
Periodic Solutions ◽  
Time Scales ◽  
Lyapunov Functional ◽  
Sufficient Conditions ◽  
Coincidence Degree ◽  
Globally Exponential Stability ◽  
Existence And Stability

Abstract By applying the method of coincidence degree and constructing a suitable Lyapunov functional, some sufficient conditions are established for the existence and globally exponential stability of periodic solutions for a kind of impulsive fuzzy Cohen- Grossberg neural networks on time scales. Moreover an example is given to illustrate our results.

scholarly journals The Method of Lyapunov Function and Exponential Stability of Impulsive Delay Systems with Delayed Impulses

2013 ◽  
Vol 2013 ◽  
pp. 1-7 ◽  
Author(s):  
Pei Cheng ◽  
Feiqi Deng ◽  
Lianglong Wang
Keyword(s):  
Lyapunov Function ◽  
Exponential Stability ◽  
Sufficient Conditions ◽  
Delay Systems ◽  
Time Varying ◽  
Matrix Inequalities ◽  
Impulsive Systems ◽  
Lyapunov Function Method ◽  
Impulsive Delay ◽  
Delayed Impulses

This paper investigates the exponential stability of general impulsive delay systems with delayed impulses. By using the Lyapunov function method, some Lyapunov-based sufficient conditions for exponential stability are derived, which are more convenient to be applied than those Razumikhin-type conditions in the literature. Their applications to linear impulsive systems with time-varying delays are also proposed, and a set of sufficient conditions for exponential stability is provided in terms of matrix inequalities. Meanwhile, two examples are discussed to illustrate the effectiveness and advantages of the results obtained.

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