Homogeneous polynomial Lyapunov functional for stability analysis of systems with delays

2018 ◽  
Author(s):  
Xingwen Liu ◽  
Yaojun Liu
Keyword(s):  
Stability Analysis ◽  
Homogeneous Polynomial ◽  
Lyapunov Functional

scholarly journals Exponential Stability of Periodic Solution to Wilson-Cowan Networks with Time-Varying Delays on Time Scales

2014 ◽  
Vol 2014 ◽  
pp. 1-10
Author(s):  
Jinxiang Cai ◽  
Zhenkun Huang ◽  
Honghua Bin
Keyword(s):  
Periodic Solution ◽  
Stability Analysis ◽  
Exponential Stability ◽  
Time Scales ◽  
Continuous Time ◽  
Lyapunov Functional ◽  
Contraction Mapping ◽  
Sufficient Conditions ◽  
Contraction Mapping Principle ◽  
Time Varying

We present stability analysis of delayed Wilson-Cowan networks on time scales. By applying the theory of calculus on time scales, the contraction mapping principle, and Lyapunov functional, new sufficient conditions are obtained to ensure the existence and exponential stability of periodic solution to the considered system. The obtained results are general and can be applied to discrete-time or continuous-time Wilson-Cowan networks.

scholarly journals Connected Stability Analysis of Delay Systems via the Matrix-Valued Lyapunov Function

2013 ◽  
Vol 313-314 ◽  
pp. 1288-1292
Author(s):  
Jian Fei Sun ◽  
Xiao Li Wang ◽  
Chen Chen
Keyword(s):  
Stability Analysis ◽  
Lyapunov Function ◽  
Comparison Theorem ◽  
Lyapunov Stability ◽  
Lyapunov Functional ◽  
Delay Systems ◽  
The Matrix

Bythe method of unioning thematrix-valued Lyapunov functional and comparison theorem,delay big system’sconnected Lyapunov stability is studied deeply.A series of new sufficientconditions are proposed.These results have not only theory meaning but alsopractical value.

Improved Results on Finite-Time Stability Analysis of Neural Networks With Time-Varying Delays

2018 ◽  
Vol 140 (10) ◽  
Author(s):  
S. Saravanan ◽  
M. Syed Ali
Keyword(s):  
Neural Networks ◽  
Stability Analysis ◽  
Finite Time ◽  
Lyapunov Functional ◽  
Convex Combination ◽  
Linear Matrix ◽  
Time Stability ◽  
Delayed Neural Networks ◽  
Finite Time Stability ◽  
Combination Methods

This paper investigates the issue of finite time stability analysis of time-delayed neural networks by introducing a new Lyapunov functional which uses the information on the delay sufficiently and an augmented Lyapunov functional which contains some triple integral terms. Some improved delay-dependent stability criteria are derived using Jensen's inequality, reciprocally convex combination methods. Then, the finite-time stability conditions are solved by the linear matrix inequalities (LMIs). Numerical examples are finally presented to verify the effectiveness of the obtained results.

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