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Stability of nonlinear Volterra equations

Ngoc P. H. A., Hieu L. T.

Bulletin of the Polish Academy of Sciences. Technical Sciences

2017

Vol. 65, nr 3

333--340

Using 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.

On Exponential Stability of Volterra Difference Equations with Infinite Delay

Ngoc P. H. A., Hieu L. T.

Bulletin of the Polish Academy of Sciences. Mathematics

2014

Vol. 62, no 2

125--137

General nonlinear Volterra difference equations with infinite delay are considered. A new explicit criterion for global exponential stability is given. Furthermore, we present a stability bound for equations subject to nonlinear perturbations. Two examples are given to illustrate the results obtained.