EAN: 9781447128519

SPRINGERBRIEFS IN ELECTRICAL AND COMPUTER ENGIN...

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.

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