Open AccessOn τ ‐decomposition frequency‐sweeping strategy to rational‐order fractional systems with commensurate delays
Author(s) -
Zhang Huaguang,
Cai Tiaoyang,
Wang Yingchun
Publication year - 2015
Publication title -
iet control theory and applications
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.059
H-Index - 108
eISSN - 1751-8652
pISSN - 1751-8644
DOI - 10.1049/iet-cta.2014.0852
Subject(s) - control theory (sociology) , order (exchange) , decomposition , fractional calculus , mathematics , computer science , control (management) , economics , artificial intelligence , finance , biology , ecology
This study presents an effective analysis procedure to give the bounded input bounded output stability intervals of time delay for a class of commensurate delayed fractional‐order systems with rational order. First, it is proposed that the analysis on multi‐valued characteristic function of delayed fractional‐order systems can be conducted equivalent on the consideration of the principal branch. The statement makes the generalisation of the τ ‐decomposition method in integer order case possible. With the convenience in studying delayed systems, the frequency‐sweeping method is applied logically, and the PIRs and the cross‐direction around them can be determined through the frequency‐sweeping curves simultaneously. Moreover, the verification of the neutral stability condition of fractional‐order delayed systems is considered in a systematic manner. At last, some examples show that the proposed strategy is practically useful in the analysis and design of feedback control for both integer and fractional‐order systems with time delays.