A proof for non existence of periodic solutions in time invariant fractional order systems

被引：160
作者：
Tavazoei, Mohammad Saleh [1 ]
Haeri, Mohammad [1 ]
机构：
[1] Sharif Univ Technol, Dept Elect Engn, Adv Control Syst Lab, Tehran 14584, Iran
来源：
AUTOMATICA | 2009年 / 45卷 / 08期
关键词：
Fractional order system; Periodic solution; Fractional calculus; LIMIT-CYCLE; CHAOS; CONTROLLERS; DERIVATIVES;
D O I：
10.1016/j.automatica.2009.04.001
中图分类号：
TP [自动化技术、计算机技术];
学科分类号：
0812 ;
摘要：
The aim of this note is to highlight one of the basic differences between fractional order and integer order systems. It is analytically shown that a time invariant fractional order system contrary to its integer order counterpart cannot generate exactly periodic signals. As a result, a limit cycle cannot be expected in the solution of these systems. Our investigation is based on Caputo's definition of the fractional order derivative and includes both the commensurate or incommensurate fractional order systems. (C) 2009 Elsevier Ltd. All rights reserved.
引用
收藏
页码：1886 / 1890
页数：5
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