Title
DistributedOrder Dynamic Systems: Stability, Simulation, Applications and Perspectives (SpringerBriefs in Electrical and Comput,Used
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Distributedorder 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 integerorder, through fractionalorder to distributedorder systems. Stability issues are addressed with graphical and numerical results highlighting the fundamental differences between constant, integer, and distributedorder treatments. The power of the distributedorder model is demonstrated with work on the stability of noncommensurateorder linear timeinvariant systems. Generic applications of the distributedorder operator follow: signal processing and viscoelastic damping of a massspring set up.A new general approach to discretization of distributedorder 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 distributedorder systems.
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