Exponential Stability Criteria for Positive Systems with Time-Varying Delay: A Delay Decomposition Technique

2015 ◽  
Vol 35 (5) ◽  
pp. 1545-1561 ◽  
Author(s):  
W. Elloumi ◽  
D. Mehdi ◽  
M. Chaabane ◽  
G. Hashim
Keyword(s):  
Exponential Stability ◽  
Time Varying ◽  
Decomposition Technique ◽  
Stability Criteria ◽  
Positive Systems ◽  
Time Varying Delay ◽  
Varying Delay ◽  
Delay Decomposition

New delay-range-dependent robust exponential stability criteria for uncertain linear systems with discrete interval and distributed time-varying delays and nonlinear perturbations

2015 ◽  
Vol 08 (03) ◽  
pp. 1550061
Author(s):  
Pornthip Somchai ◽  
Kanit Mukdasai
Keyword(s):  
Exponential Stability ◽  
Linear Systems ◽  
Time Varying ◽  
Nonlinear Perturbations ◽  
Stability Criteria ◽  
Robust Exponential Stability ◽  
Time Varying Delay ◽  
Discrete Interval ◽  
Uncertain Linear Systems ◽  
Varying Delay

In this paper, we investigate the problem of robust exponential stability analysis for uncertain linear systems with discrete interval time-varying delay, distributed time-varying delay and nonlinear perturbations. Based on constructing an augmented Lyapunov–Krasovskii functional with some parameter, decomposition technique of coefficient matrix, mixed model transformation with Leibniz–Newton formula and utilization of zero equations, new delay-range-dependent robust exponential stability criteria are derived in terms of linear matrix inequalities (LMIs). Numerical examples are given to show the superiority of our results to those in the literature.

scholarly journals A New Criterion for Exponential Stability of a Class of Hopfield Neural Network with Time-Varying Delay Based on Gronwall’s Inequality

2021 ◽  
Vol 2021 ◽  
pp. 1-9
Author(s):  
Faming Guo ◽  
Ricai Luo ◽  
Xiaolan Qin ◽  
Yunfei Yi
Keyword(s):  
Neural Network ◽  
Exponential Stability ◽  
Hopfield Neural Network ◽  
Time Varying ◽  
Stability Criteria ◽  
Time Varying Delay ◽  
Gronwall’S Inequality ◽  
Variation Of Constants ◽  
New Criterion ◽  
Varying Delay

In this paper, we study the problem of exponential stability for the Hopfield neural network with time-varying delays. Different from the existing results, we establish new stability criteria by employing the method of variation of constants and Gronwall’s integral inequality. Finally, we give several examples to show the effectiveness and applicability of the obtained criterion.

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