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Invariants and related Liapunov functions for difference equations

✍ Scribed by M.R.S Kulenović

Publisher: Elsevier Science
Year: 2000
Tongue: English
Weight: 360 KB
Volume: 13
Category: Article
ISSN: 0893-9659
DOI: 10.1016/s0893-9659(00)00068-9

No coin nor oath required. For personal study only.

✦ Synopsis

Consider the difference equation

where xn is in R k and f : D --~ D is continuous where D C R k. Suppose that I : R k ~ R is a continuous invariant, that is, I(f(x)) = I(x) for every x E D. We will show that if I attains an isolated minimum or maximum value at the equilibrium (fixed) point p of this system, then there exists a Liapunov function, namely :t=(l(x) -I(p)) and so the equilibrium p is stable. This result is then applied to some difference equations appearing in different fields of applications.

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