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 proceedingChapterpeer-review

6 Citations (Scopus)


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 languageEnglish
Title of host publicationApplications in Control
PublisherDe Gruyter
Number of pages26
ISBN (Electronic)9783110571745
ISBN (Print)9783110570908
Publication statusPublished - 1 Jan 2019


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


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