Continuous-time fractional linear systems: Steady-state responses

Duarte Valério; Manuel D. Ortigueira; J. A. Tenreiro Machado; António M. Lopes

doi:10.1515/9783110571745-007

Continuous-time fractional linear systems: Steady-state responses

Duarte Valério, Manuel D. Ortigueira, J. A. Tenreiro Machado, António M. Lopes

Research output: Chapter in Book/Report/Conference proceeding › Chapter › peer-review

7 Citations (Scopus)

Abstract

This chapter presents the frequency responses of several single-input, single-output fractional-order systems-commensurate, noncommensurate, and implicit. Both analytical expressions and the Bode, Nyquist, and Nichols diagrams are shown for several typical transfer functions. The chapter also addresses the Levy identification method for fractional orders, integer-order approximations of fractional-order systems (Crone, Carlson, Matsuda), and the Nyquist stability criterion for closed-loop commensurate systems.

Original language	English
Title of host publication	Applications in Control
Publisher	De Gruyter
Pages	149-174
Number of pages	26
ISBN (Electronic)	9783110571745
ISBN (Print)	9783110570908
DOIs	https://doi.org/10.1515/9783110571745-007
Publication status	Published - 1 Jan 2019

Keywords

Continuous-time signals and systems
Fractional calculus
Stability
State-space
Steady-state responses
Transfer function

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10.1515/9783110571745-007

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AU - Tenreiro Machado, J. A.

AU - Lopes, António M.

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AB - This chapter presents the frequency responses of several single-input, single-output fractional-order systems-commensurate, noncommensurate, and implicit. Both analytical expressions and the Bode, Nyquist, and Nichols diagrams are shown for several typical transfer functions. The chapter also addresses the Levy identification method for fractional orders, integer-order approximations of fractional-order systems (Crone, Carlson, Matsuda), and the Nyquist stability criterion for closed-loop commensurate systems.

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KW - Stability

KW - State-space

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KW - Transfer function

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Continuous-time fractional linear systems: Steady-state responses

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Keywords

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