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Stability studies for a class of nonlinear difference equations using Liapunov's Second Method

✍ Scribed by N.N. Puri; R.L. Drake

Publisher: Elsevier Science
Year: 1965
Tongue: English
Weight: 461 KB
Volume: 279
Category: Article
ISSN: 0016-0032
DOI: 10.1016/0016-0032(65)90077-3

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✦ Synopsis

In this paper a discrete analogue of Liapunov Direct Method is applied to the stability analysis of nonlinear, nonautonomous diflerence equations. A class of second and third order equations are analyzed. The Liapunov functions are generated by the use of a Routh canonical transformation. Concrete examples for the second and third order cases aTe considered. Intruduction This paper is concerned with the following nonlinear, nonautonomous difference equations : X(n + 2) + u*X(n + 1) + %X(n) + IGUn), X(n + 09 4 = 0 (11 and X(fi + 3) + a1Xb + 2) + @2X(n + 1) + asX(4 +fCXb), X@ + 11, X(n + 21, 4 = 0, (2)

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