Open AccessHow BIBO stability of LTI fractional‐order time delayed systems relates to their approximated integer‐order counterparts
Author(s) -
Nasiri Hamidreza,
Haeri Mohammad
Publication year - 2014
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.2013.0517
Subject(s) - mathematics , bibo stability , control theory (sociology) , integer (computer science) , stability (learning theory) , lti system theory , fractional order system , exponential stability , order (exchange) , fractional calculus , linear system , mathematical analysis , nonlinear system , computer science , control (management) , physics , finance , quantum mechanics , artificial intelligence , machine learning , economics , programming language
Time delay generates exponential transcendental terms in characteristic equations. Subsequently, the applied methods are narrow to assess the stability map of delayed fractional‐order systems with vanishing fractions. In this case, it is convenient to approximate these equations with its integer‐order counterparts to design controllers or investigate features of the systems. However, delay can cause enormous differences between characteristic of these two equations. This study offers a method to survey analytically the stability of fractional‐order time delayed linear time invariant systems with infinitesimal fractions. In this method, equations are transferred to an explicit expression which enables one to analyse stability of retarded, neutral and even integer‐order systems simultaneously.