Refined discretized Lyapunov functional method for systems with multiple delays

2003 ◽  
Author(s):  
Keqin Gu
Keyword(s):  
Lyapunov Functional ◽  
Functional Method ◽  
Multiple Delays ◽  
Lyapunov Functional Method

scholarly journals Global Exponential Stability of Learning-Based Fuzzy Networks on Time Scales

2015 ◽  
Vol 2015 ◽  
pp. 1-15
Author(s):  
Juan Chen ◽  
Zhenkun Huang ◽  
Jinxiang Cai
Keyword(s):  
Exponential Stability ◽  
Time Scales ◽  
Continuous Time ◽  
Lyapunov Functional ◽  
Sufficient Conditions ◽  
Functional Method ◽  
Fuzzy Neural Networks ◽  
New Learning ◽  
Fuzzy Neural ◽  
Lyapunov Functional Method

We investigate a class of fuzzy neural networks with Hebbian-type unsupervised learning on time scales. By using Lyapunov functional method, some new sufficient conditions are derived to ensure learning dynamics and exponential stability of fuzzy networks on time scales. Our results are general and can include continuous-time learning-based fuzzy networks and corresponding discrete-time analogues. Moreover, our results reveal some new learning behavior of fuzzy synapses on time scales which are seldom discussed in the literature.

scholarly journals Periodic Solution for Impulsive Cellar Neural Networks with Time-Varying Delays in the Leakage Terms

2013 ◽  
Vol 2013 ◽  
pp. 1-10 ◽  
Author(s):  
Bingwen Liu ◽  
Shuhua Gong
Keyword(s):  
Neural Networks ◽  
Periodic Solution ◽  
Differential Inequality ◽  
Lyapunov Functional ◽  
Sufficient Conditions ◽  
Functional Method ◽  
Time Varying ◽  
Activation Functions ◽  
Lyapunov Functional Method ◽  
Inequality Techniques

This paper is concerned with impulsive cellular neural networks with time-varying delays in leakage terms. Without assuming bounded and monotone conditions on activation functions, we establish sufficient conditions on existence and exponential stability of periodic solutions by using Lyapunov functional method and differential inequality techniques. Our results are complement to some recent ones.

scholarly journals Periodic solution for inertial neural networks with variable parameters

2021 ◽  
Vol 6 (12) ◽  
pp. 13580-13591
Author(s):  
Lingping Zhang ◽  
◽  
Bo Du
Keyword(s):  
Neural Networks ◽  
Periodic Solution ◽  
Asymptotic Stability ◽  
Lyapunov Functional ◽  
Sufficient Conditions ◽  
Functional Method ◽  
Mawhin’S Continuation Theorem ◽  
Variable Parameters ◽  
Inertial Neural Networks ◽  
Lyapunov Functional Method

<abstract><p>We discuss periodic solution problems and asymptotic stability for inertial neural networks with $ D- $operator and variable parameters. Based on Mawhin's continuation theorem and Lyapunov functional method, some new sufficient conditions on the existence and asymptotic stability of periodic solutions are established. Finally, a numerical example verifies the effectiveness of the obtained results.</p></abstract>

scholarly journals A Novel Stability Analysis of Uncertain Switched Systems with Time-Varying Delays

2015 ◽  
Vol 2015 ◽  
pp. 1-7 ◽  
Author(s):  
Ganji Huang ◽  
Shixian Luo ◽  
Linna Wei ◽  
Wuhua Chen
Keyword(s):  
Switched Systems ◽  
Lyapunov Functional ◽  
Sufficient Conditions ◽  
Functional Method ◽  
Time Varying ◽  
System Parameters ◽  
Time Varying Delay ◽  
Lyapunov Functional Method ◽  
The Stability ◽  
Varying Delay

This paper deals with the stability of switched systems with time-varying delay. The time-varying system parameters are assumed to be norm-bounded. Based on a novel switched time-varying Lyapunov functional method, some new LMI-based sufficient conditions have been obtained to ensure the exponential stability for the uncertain switched delays systems. Finally, the proposed method is applied to a numerical example and the simulative results are also given.

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