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Exponential Stability Criteria for Nonautonomous Difference Systems

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  • Rigoberto Medina

Abstract

The aim of this paper is to characterize the exponential stability of linear systems of difference equations with slowly varying coefficients. Our approach is based on the generalization of the freezing method for difference equations combined with new estimates for the norm of bounded linear operators. The main novelty of this work is that we use estimates for the absolute values of entries of a matrix-valued function, instead of bounds on its eigenvalues. By this method, new explicit stability criteria for linear nonautonomous systems are derived.

Suggested Citation

  • Rigoberto Medina, 2014. "Exponential Stability Criteria for Nonautonomous Difference Systems," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 2014, pages 1-7, April.
    • Handle: RePEc:hin:jijmms:206343
    DOI: 10.1155/2014/206343
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    1. Rigoberto Medina & M. I. Gil', 2004. "Accurate solution estimates for nonlinear nonautonomous vector difference equations," Abstract and Applied Analysis, Hindawi, vol. 2004, pages 1-9, January.
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