scholarly journals Stability of nonlinear Volterra equations

2017 ◽  
Vol 65 (3) ◽  
pp. 333-340
Author(s):  
P. H. A. Ngoc ◽  
L. T. Hieu
Keyword(s):  
Global Exponential Stability ◽  
Zero Solution ◽  
Volterra Equations ◽  
Time Varying ◽  
Bidirectional Associative Memory ◽  
Stability Bound ◽  
Novel Approach ◽  
Nonlinear Volterra Equations ◽  
Volterra Difference Equations ◽  
Explicit Criteria

AbstractUsing a novel approach, we present some new explicit criteria for global exponential stability of the zero solution of general nonlinear time-varying Volterra difference equations. Furthermore, an explicit stability bound for equations subject to nonlinear time-varying perturbations is given. Finally, the obtained results are used to study uniform attraction of equilibrium of discrete-time bidirectional associative memory (BAM) neural networks. Some illustrative examples are given.

New criteria for global exponential stability of linear time-varying volterra difference equations

2016 ◽  
Vol 66 (6) ◽  
Author(s):  
Trung Hieu Le
Keyword(s):  
Exponential Stability ◽  
Difference Equations ◽  
Global Exponential Stability ◽  
Linear Time ◽  
Time Varying ◽  
Novel Approach ◽  
New Criteria ◽  
Volterra Difference Equations ◽  
Explicit Criteria

AbstractLinear time-varying Volterra difference equations are considered. By a novel approach, we get some new explicit criteria for global exponential stability. Some examples are given to illustrate the obtained results. To the best of our knowledge, the obtained results are new.

scholarly journals Global Exponential Stability Criteria for Bidirectional Associative Memory Neural Networks with Time-Varying Delays

2013 ◽  
Vol 2013 ◽  
pp. 1-13 ◽  
Author(s):  
J. Thipcha ◽  
P. Niamsup
Keyword(s):  
Neural Networks ◽  
Exponential Stability ◽  
Associative Memory ◽  
Global Exponential Stability ◽  
Linear Matrix ◽  
Time Varying ◽  
Stability Criteria ◽  
Bidirectional Associative Memory ◽  
Lower And Upper Bounds ◽  
Delay Dependent

The global exponential stability for bidirectional associative memory neural networks with time-varying delays is studied. In our study, the lower and upper bounds of the activation functions are allowed to be either positive, negative, or zero. By constructing new and improved Lyapunov-Krasovskii functional and introducing free-weighting matrices, a new and improved delay-dependent exponential stability for BAM neural networks with time-varying delays is derived in the form of linear matrix inequality (LMI). Numerical examples are given to demonstrate that the derived condition is less conservative than some existing results given in the literature.

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