Advanced Search

Query:

Fill in the form and click »Search«...

Format:

Display: entries per page entries

Zbl 1067.39012
Matsunaga, Hideaki
Stability regions for a class of delay difference systems. (English)
[A] Elaydi, Saber (ed.) et al., Difference and differential equations. Proceedings of the 7th international conference on difference equations and applications (ICDEA), Changsha, China, August 12--17, 2002. Providence, RI: American Mathematical Society (AMS). Fields Institute Communications 42, 273-283 (2004). ISBN 0-8218-3354-5/hbk

Summary: We give some new necessary and sufficient conditions for the asymptotic stability of a linear delay difference system $$x_{n+1}- ax_n+ Bx_{n-k}= 0,\quad n= 0,1,2,\dots,\tag L$$ by using root-analysis or its characteristic equation. Here, $a$ is a real number, $B$ is a $2\times 2$ real constant matrix, and $k$ is a positive integer. In case $$B= b\pmatrix \cos\theta &-\sin\theta\\ \sin\theta & \cos\theta\endpmatrix,\quad b\in\bbfR,\ |\theta|\le{\pi\over 2},$$ the stability region for (L), that is, the region of $(a, b)$ for which the zero solution of (L) with fixed $k$ and $\theta$ is asymptotically stable, is symmetric with respect to the $b$-axis (resp. origin) if $k$ is odd (resp. even).

MSC 2000:: *39A11 Stability of difference equations

Keywords: asymptotic stability; linear delay difference system

Comment on this Item PDF MathML XML ASCII DVI PS BibTeX Online Ordering

	Scientific prize winners of the ICM 2010
	Overhang
	Lie groups, physics and geometry. An introduction for physicists, engineers and chemists.

Advanced Search

Zentralblatt MATH Berlin [Germany]