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.
Duo-Qing Sun. Zhu-Mei Sun. "Asymptotic Stability of the Golden-Section Control Law for Multi-Input and Multi-Output Linear Systems." J. Appl. Math. 2012 1 - 11, 2012. https://doi.org/10.1155/2012/407409