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Additional resources 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

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To begin a study of fractional systems we need to define fractional derivative. The most obvious approach for fractional derivative is the Grünwald-Letnikov method that is a generalisation of the usual definition based on the incremental ratio [1-3]. However, it is very hard to manipulate and obtain new results. This motivates us to adopt a definition based on the Laplace Transforms. Consider first the Laplace Transform (LT) case. Essentially, we shall be looking for the Laplace Inverse Transform of sα, δ(α)(t), with α being any positive real number.

3) can represent an infinite number of linear systems. However, only the principal Riemann surface, {z: -π≤ arg(z)<π}, may lead to a real system. Constraining this function by imposing a region of convergence, we define a transfer function. 6) gives the corresponding impulse response. Now, go a step ahead and consider the simple case corresponding to the fraction 41st IEEE CONFERENCE ON DECISION AND CONTROL 47 TUTORIAL WORKSHOP #2. 4) where ν is a real number. The equation s ν = a has infinite solutions that are on a circle of radius |a|1/ν .

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