Vol.2, No 7, 1997 pp. 325-329
UDC 681.511.4
A QUALITATIVE METHOD FOR STABILITY ANALYSIS
OF NONLINEAR DISCRETE DYNAMICAL SYSTEMS
Bratislav Danković1,
Miomir Stanković2
1Faculty
of Electronic Engineering, Niš Yugoslavia
2Faculty
of Occupational Safety, Niš Yugoslavia
Abstract. Main results are presented by two theorems determining
sufficient conditions for stability, and necessary conditions for instability
of equilibrium point of a nonlinear discrete dynamical system. By introducing
the concept of discrete divergence as a difference operator, a discrete
analogue of the Liuvill theorem on expansion of phase volume was derived.
This theorem was a base for the derivation of the presented results.
Key words: Stability, nonlinear system, discrete system, field
theory, diveregence.
KVALITATIVNI
METOD ZA ANALIZU STABILNOSTI NELINEARNIH DISKRETNIH SISTEMA
U radu je izložen jedan nov metod za kvalitativnu
analizu stabilnosti nelinearnih diskretnih sistema baziran na diskretnoj
teoriji polja. Uveden je pojam diskretne diveregencije u vidu diferencnog
operatora. Dat je diskretan analog Luivilove teoreme o širenju diskretnog
faznog prostora. Glavni rezultati su dati u vidu dve teoreme o potrebnim
uslovima za stabilnost i dovoljnim uslovima za nestabilnost diskretnih
sistema.
