Robust stability test of a class of linear time-invariant interval fractional-order system using Lyapunov inequality

Abstract

This paper provides a new analytical robust stability checking method of fractional-order linear time invariant interval uncertain system. This paper continues the authors’ previous work [YangQuan Chen, Hyo-Sung Ahn, I. Podlubny, Robust stability check of fractional-order linear time invariant systems with interval uncertainties, in: Proceedings of the IEEE Conference on Mechatronics and Automation, Niagara Falls, Canada, July, 2005, pp. 210–215] where matrix perturbation theory was used. For the new robust stability checking, Lyapunov inequality is utilized for finding the maximum eigenvalue of a Hermitian matrix. Through numerical examples, the usefulness and the effectiveness of the newly proposed method are verified.