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On linear systems with a fractional derivation: Introductory theory and examples

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  • Hotzel, Richard
  • Fliess, Michel

Abstract

Linear systems with a derivation of non-integer order are examined as a special case of systems described by Mikusiński operators. Controllability and observability are examined using the theory of modules, as well as regulation of finite-dimensional systems. A stability result is obtained based upon the asymptotic properties of generalized Mittag-Leffler exponents. A solution of the tracking problem for σ-controllable fractional delay systems is presented. The article includes examples of a finite-dimensional fractional system and a fractional delay system.

Suggested Citation

  • Hotzel, Richard & Fliess, Michel, 1998. "On linear systems with a fractional derivation: Introductory theory and examples," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 45(3), pages 385-395.
    • Handle: RePEc:eee:matcom:v:45:y:1998:i:3:p:385-395
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