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Some Bounds on Maximum Number of Frequencies Existing in Oscillations Produced by Linear Fractional Order Systems

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Abstract

In this paper, it has been studied that how the inner dimension of a fractional order system influences the maximum number of frequencies which may exist in oscillations produced by this system. Both commensurate and incommensurate systems have been considered to clarify the relationship between the inner dimension and maximum number of frequencies. It has been shown that although in commensurate fractional order systems, like integer order systems, the maximum number of frequencies is half of the inner dimension, in incommensurate systems the problem is significantly more complicated and the relationship between the inner dimension and maximum frequencies can not precisely determined. However, in this article, some upper and lower bounds, depending on the inner dimension, have been provided for the maximum frequencies of incommensurate systems.

Keywords

Stability Boundary Order System Fractional Order System Undamped Oscillation Integer Order System 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer Science+Business Media B.V. 2010

Authors and Affiliations

  1. 1.Advanced Control System Lab., Electrical Engineering DepartmentSharif University of TechnologyTehranIran

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