By Blas M. Vinagre, YangQuan Chen (Eds.)

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Read or Download 41st IEEE Conference on Decision and Control, Tutorial Workshop No. 2: Fractional Calculus Applications in Automatic Control and Robotics (Las Vegas, USA, December 9, 2002): Lecture Notes PDF

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Additional info for 41st IEEE Conference on Decision and Control, Tutorial Workshop No. 2: Fractional Calculus Applications in Automatic Control and Robotics (Las Vegas, USA, December 9, 2002): Lecture Notes

Sample text

It is interesting to remark that the asymptotic amplitude Bode diagrams are constituted by straight lines with slopes that, at least in principle, may assume any value, contrarily to the usual case where the slopes are multiples of 20 dB/decade. 1. 2). 2. From the Transfer Function to the Impulse Response To obtain the Impulse Response from the Transfer Function we proceed almost as usually. However, we must be careful. 3) α s is a multivalued expression defining an infinite number of Riemann surfaces.

This idea was recovered, later, by Grünwald (1867) and Letnikov (1868). 1) for the fractional integral. Holmgren (1865/66) and Letnikov (1868/74) discussed that problem when looking for the solution of differential equations, putting in a correct statement the fractional differentiation as inverse operation of the fractional integration. Hadamard proposed a method of fractional differentiation based on the differentiation of Taylor´s series associated with the function, Weyl (1917) defined a fractional integration suitable to periodic functions and Marchaud (1927) presented a new form of differentiation based on finite differences.

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41st IEEE Conference on Decision and Control, Tutorial Workshop No. 2: Fractional Calculus Applications in Automatic Control and Robotics (Las Vegas, USA, December 9, 2002): Lecture Notes by Blas M. Vinagre, YangQuan Chen (Eds.)


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