Distributed-Order Dynamic Systems

Beschreibung

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 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.
Shows the reader original results in stability analysis of linear time-invariant systems connected with distributed-order dynamic systems Provides the reader with a general approach to the use of distributed-order operators for use in a number of scientific and engineering disciplines MATLAB® codes expedite the repetitive coding of the examples in the Brief allowing the new user to get started quickly Includes supplementary material: sn.pub/extras

Autor*in

Zhuang Jiao

Themen in »Distributed-Order Dynamic 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

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From the book reviews:

“This book is a concise introduction to the theory and use of distributed-order systems. … Written at the level of first- or second-year graduate student, the book is well suited as a self-contained introduction to an emerging area of research and applications.” (IEEE Control Systems Magazine, October, 2013)

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