Distributed-Order Dynamic Systems

Stability, Simulation, Applications and Perspectives

  • Zhuang Jiao
  • YangQuan Chen
  • Igor Podlubny

Part of the SpringerBriefs in Electrical and Computer Engineering book series (BRIEFSELECTRIC)

Also part of the SpringerBriefs in Control, Automation and Robotics book sub series (BRIEFSCONTROL)

Table of contents

  1. Front Matter
    Pages i-xiii
  2. Zhuang Jiao, YangQuan Chen, Igor Podlubny
    Pages 1-10
  3. Zhuang Jiao, YangQuan Chen, Igor Podlubny
    Pages 11-28
  4. Zhuang Jiao, YangQuan Chen, Igor Podlubny
    Pages 29-37
  5. Zhuang Jiao, YangQuan Chen, Igor Podlubny
    Pages 39-58
  6. Zhuang Jiao, YangQuan Chen, Igor Podlubny
    Pages 59-74
  7. Zhuang Jiao, YangQuan Chen, Igor Podlubny
    Pages 75-79
  8. Back Matter
    Pages 81-90

About this book


Distributed-order differential equations, a generalization of fractional calculus, are of increasing importance in many fields of science and engineering from the behaviour of complex dielectric media to the modelling of nonlinear systems.
This Brief will broaden the toolbox available to researchers interested in modeling, analysis, control and filtering. It contains contextual material outlining the progression from integer-order, through fractional-order to distributed-order systems. Stability issues are addressed with graphical and numerical results highlighting the fundamental differences between constant-, integer-, and distributed-order treatments. The power of the distributed-order model is demonstrated with work on the stability of noncommensurate-order linear time-invariant systems. Generic applications of the distributed-order operator follow: signal processing and viscoelastic damping of a mass–spring set up.
A new general approach to discretization of distributed-order derivatives and integrals is described. The Brief is rounded out with a consideration of likely future research and applications and with a number of MATLAB® codes to reduce repetitive coding tasks and encourage new workers in distributed-order systems.


Distributed-order Control Distributed-order Linear Time-invariant Systems Distributed-order Modelling Distributed-order Signal Processing Fractional-order systems Numerical Solution of Distributed-order Equations

Authors and affiliations

  • Zhuang Jiao
    • 1
  • YangQuan Chen
    • 2
  • Igor Podlubny
    • 3
  1. 1., Department of AutomationTsinghua UniversityBeijingChina, People's Republic
  2. 2., Department of Electrical and ComputerUtah State UniversityLoganUSA
  3. 3., BERG FacultyTechnical University of KosiceKosiceSlovakia

Bibliographic information

  • DOI
  • Copyright Information The Author(s) 2012
  • Publisher Name Springer, London
  • eBook Packages Engineering
  • Print ISBN 978-1-4471-2851-9
  • Online ISBN 978-1-4471-2852-6
  • Series Print ISSN 2191-8112
  • Series Online ISSN 2191-8120
  • Buy this book on publisher's site