Tuyển tập báo cáo các nghiên cứu khoa học quốc tế ngành hóa học dành cho các bạn yêu hóa học tham khảo đề tài: Research Article Annular Bounds for Polynomial Zeros and Schur Stability of Difference Equations | Hindawi Publishing Corporation Advances in Difference Equations Volume 2011 Article ID 782057 11 pages doi 2011 782057 Research Article Annular Bounds for Polynomial Zeros and Schur Stability of Difference Equations Ke Li1 and Jin Liang2 1 Shandong Key Laboratory of Automotive Electronic Technology Institute of Automation Shandong Academy of Sciences Jinan Shandong 250014 China 2 Department of Mathematics Shanghai Jiao Tong University Shanghai 200240 China Correspondence should be addressed to Jin Liang jinliang@ Received 7 October 2010 Accepted 30 October 2010 Academic Editor Toka Diagana Copyright 2011 K. Li and J. 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. We investigate the monic complex-coefficient polynomial of degree n f z zn an-1zn-1 a0 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. 1. Introduction It is well known that many discrete-time systems in engineering are described in terms of a difference equation and the characteristic equation for the difference equation plays a key role in the study of the behaviors of the solutions especially the stability of the solutions to the discrete-time systems. Since the characteristic equations for difference equations are closely related to some complex polynomials the estimates of the bound for the moduli of various complex polynomial zeros have been investigated by many researchers cf. . 18 and references therein . In the study on this issue one of meaningful research ideas is to indicate such a common property of a lot of polynomials by a few very special polynomials. Using this idea a good annular .
