LMI stability conditions for fractional order systems

被引：355
作者：
Sabatier, Jocelyn [1 ]
Moze, Mathieu [1 ]
Farges, Christophe [1 ]
机构：
[1] Univ Bordeaux 1, CNRS, IMS Lab, LAPS CRONE Grp,UMR 5218, F-33405 Talence, France
来源：
COMPUTERS & MATHEMATICS WITH APPLICATIONS | 2010年 / 59卷 / 05期
关键词：
Fractional systems; Stability; Linear Matrix Inequalities; ROBUST STABILITY; DELAY SYSTEMS;
D O I：
10.1016/j.camwa.2009.08.003
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
After an overview of the results dedicated to stability analysis of systems described by differential equations involving fractional derivatives, also denoted fractional order systems, this paper deals with Linear Matrix Inequality (LMI) stability conditions for fractional order systems. Under commensurate order hypothesis, it is shown that a direct extension of the second Lyapunov's method is a tedious task. If the fractional order v is such that 0 nu < 1, the stability domain is not a convex region of the complex plane. However, through a direct stability domain characterization, three LMI stability analysis conditions are proposed. The first one is based on the stability domain deformation and the second one on a characterization of the instability domain (which is convex). The third one is based on generalized LMI framework. These conditions are applied to the gain margin computation of a CRONE suspension. (C) 2009 Elsevier Ltd. All rights reserved.
引用
收藏
页码：1594 / 1609
页数：16
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