Journal of Applied Mathematics
Volume 2012 (2012), Article ID 407409, 11 pages
http://dx.doi.org/10.1155/2012/407409
Research Article

Asymptotic Stability of the Golden-Section Control Law for Multi-Input and Multi-Output Linear Systems

Duo-Qing Sun1,2 and Zhu-Mei Sun3

1Institute of Mathematics and Systems Science, Hebei Normal University of Science and Technology, Qinhuangdao 066004, China
2Beijing Institute of Control Engineering, China Academy of Space Technology, Beijing 100190, China
3School of Optoelectronics, Beijing Institute of Technology, Beijing 100081, China

Received 16 September 2011; Accepted 19 December 2011

Academic Editor: Mark A. Petersen

Copyright © 2012 Duo-Qing Sun and Zhu-Mei Sun. 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

This paper is concerned with the problem of the asymptotic stability of the characteristic model-based golden-section control law for multi-input and multi-output linear systems. First, by choosing a set of polynomial matrices of the objective function of the generalized least-square control, we prove that the control law of the generalized least square can become the characteristic model-based golden-section control law. Then, based on both the stability result of the generalized least-square control system and the stability theory of matrix polynomial, the asymptotic stability of the closed loop system for the characteristic model under the control of the golden-section control law is proved for minimum phase system.