Continuous-time fractional linear systems: Transient responses

Manuel D. Ortigueira, Duarte Valério, António M. Lopes

Research output: Chapter in Book/Report/Conference proceedingChapterpeer-review


This chapter presents an introduction to fractional continuous-time linear systems, based on suitable fractional derivatives. The usual tools, impulse response, transfer function, and frequency responses are defined, and the manner of their computation is given, considering both commensurate and noncommensurate cases. Properties of the systems, like causality, periodicity, and stability are also studied. The formulation in the commensurate case is done in a full agreement with classic results that are recovered when the derivative order becomes equal to 1. Multiple-input, multiple-output systems are also studied from the state-space point of view.

Original languageEnglish
Title of host publicationApplications in Control
PublisherDe Gruyter
Number of pages30
ISBN (Electronic)9783110571745
ISBN (Print)9783110570908
Publication statusPublished - 1 Jan 2019


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


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