Advances in Difference Equations
Volume 2011 (2011), Article ID 782057, 11 pages
doi:10.1155/2011/782057
Research Article

Annular Bounds for Polynomial Zeros and Schur Stability of Difference Equations

Ke Li1 and Jin Liang2

1Shandong Key Laboratory of Automotive Electronic Technology, Institute of Automation, Shandong Academy of Sciences, Jinan, Shandong 250014, China
2Department of Mathematics, Shanghai Jiao Tong University, Shanghai 200240, China

Received 7 October 2010; Accepted 30 October 2010

Academic Editor: Toka Diagana

Copyright © 2011 Ke Li and Jin Liang. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We investigate the monic complex-coefficient polynomial of degree 𝑛 , 𝑓 ( 𝑧 ) ∶ = 𝑧 𝑛 + 𝑎 𝑛 − 1 𝑧 𝑛 − 1 + ⋯ + 𝑎 0 in the complex variable 𝑧 and obtain a new annular bound for the zeros of 𝑓 ( 𝑧 ) , which is sharper than the previous results and has clear advantages in judging the Schur stability of difference equations. In addition, examples are given to illustrate the theoretical result.