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 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.

scholarly journals Impulsive Disturbances on the Dynamical Behavior of Complex-Valued Cohen-Grossberg Neural Networks with Both Time-Varying Delays and Continuously Distributed Delays

Complexity ◽  
2017 ◽  
Vol 2017 ◽  
pp. 1-12 ◽  
Author(s):  
Xiaohui Xu ◽  
Jiye Zhang ◽  
Quan Xu ◽  
Zilong Chen ◽  
Weifan Zheng
Keyword(s):  
Neural Networks ◽  
Exponential Stability ◽  
Equilibrium Point ◽  
Global Exponential Stability ◽  
Dynamical Behavior ◽  
Sufficient Conditions ◽  
Distributed Delays ◽  
Time Varying ◽  
Homeomorphism Mapping ◽  
Complex Valued

This paper studies the global exponential stability for a class of impulsive disturbance complex-valued Cohen-Grossberg neural networks with both time-varying delays and continuously distributed delays. Firstly, the existence and uniqueness of the equilibrium point of the system are analyzed by using the corresponding property of M-matrix and the theorem of homeomorphism mapping. Secondly, the global exponential stability of the equilibrium point of the system is studied by applying the vector Lyapunov function method and the mathematical induction method. The established sufficient conditions show the effects of both delays and impulsive strength on the exponential convergence rate. The obtained results in this paper are with a lower level of conservatism in comparison with some existing ones. Finally, three numerical examples with simulation results are given to illustrate the correctness of the proposed results.

Sign in / Sign up

Export Citation Format

Share Document