The Stability Cone for a Matrix Delay Difference Equation

M. M. Kipnis and V. V. Malygina

International Journal of Mathematics and Mathematical Sciences, 2011, vol. 2011, 1-15

Abstract:

We construct a stability cone, which allows us to analyze the stability of the matrix delay difference equation ð ‘¥ ð ‘› = ð ´ ð ‘¥ ð ‘› − 1 + ð µ ð ‘¥ ð ‘› − 𠑘 . We assume that ð ´ and ð µ are ð ‘š × ð ‘š simultaneously triangularizable matrices. We construct ð ‘š points in â„ 3 which are functions of eigenvalues of matrices ð ´ , ð µ such that the equation is asymptotically stable if and only if all the points lie inside the stability cone.

Date: 2011
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:860326

DOI: 10.1155/2011/860326

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