TY - JOUR
T1 - The 21st Century Systems
T2 - An Updated Vision of Continuous-Time Fractional Models
AU - Ortigueira, Manuel Duarte
AU - Machado, J. Tenreiro
N1 - Publisher Copyright:
© 2022 Institute of Electrical and Electronics Engineers Inc.. All rights reserved.
info:eu-repo/grantAgreement/FCT/6817 - DCRRNI ID/UIDB%2F00066%2F2020/PT#
A few days before the end of the revision procedure, my friend J. Tenreiro Machado had a sudden cardio-respiratory arrest and died. Here I want to express my gratitude and tribute to a great man and scientist. He was a very friendly and helpful person, with an unusual work capacity that allowed him to publish interesting articles on a wide range of topics.
PY - 2022
Y1 - 2022
N2 - This paper presents the continuous-time fractional linear systems and their main properties. Two particular classes of models are introduced: the fractional autoregressive-moving average type and the tempered linear system. For both classes, the computations of the impulse response, transfer function, and frequency response are discussed. It is shown that such systems can have integer and fractional components. From the integer component we deduce the stability. The fractional order component is always stable. The initial-condition problem is analyzed and it is verified that it depends on the structure of the system. For a correct definition and backward compatibility with classic systems, suitable fractional derivatives are also introduced. The Grünwald-Letnikov and Liouville derivatives, as well as the corresponding tempered versions, are formulated.
AB - This paper presents the continuous-time fractional linear systems and their main properties. Two particular classes of models are introduced: the fractional autoregressive-moving average type and the tempered linear system. For both classes, the computations of the impulse response, transfer function, and frequency response are discussed. It is shown that such systems can have integer and fractional components. From the integer component we deduce the stability. The fractional order component is always stable. The initial-condition problem is analyzed and it is verified that it depends on the structure of the system. For a correct definition and backward compatibility with classic systems, suitable fractional derivatives are also introduced. The Grünwald-Letnikov and Liouville derivatives, as well as the corresponding tempered versions, are formulated.
UR - http://www.scopus.com/inward/record.url?scp=85131302080&partnerID=8YFLogxK
U2 - 10.1109/MCAS.2022.3160905
DO - 10.1109/MCAS.2022.3160905
M3 - Article
AN - SCOPUS:85131302080
SN - 1531-636X
VL - 22
SP - 36
EP - 56
JO - IEEE Circuits and Systems Magazine
JF - IEEE Circuits and Systems Magazine
IS - 2
ER -