Document Type
Post-Print
Publication Date
6-15-2009
Abstract
We survey some of the fundamental results on the stability and asymptoticity of linear Volterra difference equations. The method of Ζ-transform is heavily utilized in equations of convolution type. An example is given to show that uniform asymptotic stability does not necessarily imply exponential stabilty. It is shown that the two notions are equivalent if the kernel decays exponentially. For equations of nonconvolution type, Liapunov functions are used to find explicit criteria for stability. Moreover, the resolvent matrix is defined to produce a variation of constants formula. The study of asymptotic equivalence for difference equations with infinite delay is carried out in Section 6. Finally, we state some problems.
Identifier
10.1016/j.cam.2008.03.023
Publisher
Elsevier B.V.
Repository Citation
Elaydi, S. (2009). Stability and asymptoticity of Volterra difference equations: A progress report. Journal of Computational and Applied Mathematics, 228(2), 504-513. doi:10.1016/j.cam.2008.03.023
Publication Information
Journal of Computational and Applied Mathematics