Selçuk Journal of Applied Mathematics

www.selcuk.edu.tr




 Selçuk Journal of
  Applied Mathematics

SPECIAL ISSUE

 
Summer-Autumn, 2001
  Volume  2
  Number 2

 
Research Center of 
  Applied Mathematics


 SJAM Summer-Autumn 2001, Volume 2 - Number 2

Continuity of numeric characteristics for asymptotic stability of solutions to linear difference equations with periodic coefficients
Kemal Aydın1, Haydar Bulgak1, Gennadii Demidenko2*
1 Research Centre of Applied Mathematics, Selçuk University, Konya, Turkey
   email : hbulgak@selcuk.edu.tr  ; kaydin@selcuk.edu.tr

2 Sobolev Institute of Mathematics, SB RAS, Novosibirsk, Russia;
  email: demidenk@math.nsc.ru

Received: May 21, 2001
 

Summary.  

We consider linear perturbation systems of difference equations

y(n+1)=(A(n) + B(n))y(n), n³ 0, where A(n), B(n) are N´N periodic matrices with period  T. The spectrum of a monodromy matrix of the system x(n+1)=A(n)x(n),
n
³ 0 belongs to the unit disk

|l| < 1. We indicate conditions on a perturbation matrix B(n)  for asymptotic stability of the zero solution to the perturbation system and prove continuity one numeric characteristic of the asymptotic stability from [1].


 

Key words
monodromy matrix, perturbation systems of difference equations, asymptotic stability of solutions.
 

Mathematics Subject Classification (1991): 39A11

* The research was financially supported by the Scientific and Technical Research Council of Turkey (TUBITAK) in the framework of a NATO-PC Advanced Fellowships Programme.

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