Geodesic
A stability condition for nth order difference equations
Glasgow mathematical journal, Tome 12 (1971) no. 1, pp. 24-30

Voir la notice de l'article provenant de la source Cambridge University Press

Consider the system of difference equationsin which the unknown x(t) is a complex m-vector, t is a real variable and a1, ..., an are complex m × m matrices whose elements are functions of t, x(t), x(t+1), ..., x(t+n – 1). A positive definite hermitian form V(x1x2, ..., xn), with constant coefficients, is called a strong autonomous quadratic Lyapunov function (written strong AQLF) of (1) if there exists a constant K > 1 such that K2v(t+1) < v(t) for all non-zero solutions x(t)of (1), where v(t) = V(x(t), x(t+ 1), ..., x(t+n —1)). The existence of a strong AQLF is a sufficient condition for the trivial solution x =0 of (1) to be globally asymptotically stable. It is a necessary condition only in the special case of an equation 
Smith, Russell A. A stability condition for nth order difference equations. Glasgow mathematical journal, Tome 12 (1971) no. 1, pp. 24-30. doi: 10.1017/S0017089500001105
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[1] 1.Skachkov, B. N., On the stability of the zero solution of a class of nth order differential equations (Russian), Differencial'nve Uravnenija 1 (1965), 171–175. English translation: Differential Equations1 (1965), 126–129. Google Scholar

[2] 2.Smith, R. A., Mobius transformations in stability theory, Proc. Cambridge Phil. Soc. 68 (1970), 143–151. Google Scholar | DOI

[3] 3.Stoer, J. and Witzgall, C., Transformation by diagonal matrices in a normed space, Numerische Math. 4 (1962), 158–171. Google Scholar | DOI

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