An introduction to difference equations
An introduction to difference equations
Global stability of difference equations
WCNA '92 Proceedings of the first world congress on World congress of nonlinear analysts '92, volume II
Volterra Integral and Differential Equations: SECOND EDITION (Mathematics in Science and Engineering)
Structured stability radii and exponential stability tests for Volterra difference systems
Computers & Mathematics with Applications
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We survey some of the fundamental results on the stability and asymptoticity of linear Volterra difference equations. The method of Z-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.