Stabilization and Control of Fractional Order Systems: A by Bijnan Bandyopadhyay, Visit Amazon's Shyam Kamal Page, PDF

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By Bijnan Bandyopadhyay, Visit Amazon's Shyam Kamal Page, search results, Learn about Author Central, Shyam Kamal,

In the final 20 years fractional differential equations were used extra usually in physics, sign processing, fluid mechanics, viscoelasticity, mathematical biology, electro chemistry and so forth. It opens a brand new and extra practical technique to catch reminiscence established phenomena and irregularities contained in the structures through the use of extra subtle mathematical analysis.

This monograph relies at the authors’ paintings on stabilization and regulate layout for non-stop and discrete fractional order platforms. The preliminary chapters and a few elements of the 3rd bankruptcy are written in educational type, providing the entire simple thoughts of fractional order method and a short evaluation of sliding mode keep an eye on of fractional order structures. the opposite components comprise take care of strong finite time balance of fractional order structures, crucial sliding mode regulate of fractional order structures, co-operative keep an eye on of multi-agent platforms modeled as fractional differential equation, powerful stabilization of discrete fractional order structures, excessive functionality regulate utilizing delicate variable constitution regulate and contraction research via integer and fractional order infinitesimal variations.

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Extra resources for Stabilization and Control of Fractional Order Systems: A Sliding Mode Approach

Example text

From the above example, x (1) doesn’t exist but R L derivative exists at t = 1. 25) x(t) = 0 if t = 1 ⎪ ⎩ 2 − t if 1 < t < 2. Then, if 0 < α < 1, we get ⎧ ⎪ ⎪ ⎨ t 1−α if 0 < t < 1 Γ (2 − α) RL α D x(t) = t 0 t 1−α − 2(t − 1)1−α ⎪ ⎪ ⎩ if 1 < t < 2. Γ (2 − α) Therefore, lim t = 1. 26) 1 R α Γ (2−α) . Then 0 L Dt x(t) exists at Example Riemann-Liouville derivative of the Weierstrass function (continuous everywhere but differentiable nowhere in classical sense) as shown in Fig. 8. One form of Weierstrass function is as follows [11] λ−μj sin(λ j t), (0 < μ < 1, λ > 1).

25) x(t) = 0 if t = 1 ⎪ ⎩ 2 − t if 1 < t < 2. Then, if 0 < α < 1, we get ⎧ ⎪ ⎪ ⎨ t 1−α if 0 < t < 1 Γ (2 − α) RL α D x(t) = t 0 t 1−α − 2(t − 1)1−α ⎪ ⎪ ⎩ if 1 < t < 2. Γ (2 − α) Therefore, lim t = 1. 26) 1 R α Γ (2−α) . Then 0 L Dt x(t) exists at Example Riemann-Liouville derivative of the Weierstrass function (continuous everywhere but differentiable nowhere in classical sense) as shown in Fig. 8. One form of Weierstrass function is as follows [11] λ−μj sin(λ j t), (0 < μ < 1, λ > 1). 3 Why Fractional Order?

After looking into the literature towards we are able to find one important work which is presented by Blas M. Vinagre and YangQuan Chen [5], 41st IEEE CDC-2002 tutorial workshop. This gives lots of motivation to us, to work and try to bring more researchers, academicians and industrial people towards this area, particularly fractional order system in the science and control engineering disciple. Before moving towards fractional order modeling and control a lot of restrictions of classical calculus is pointed out by Blas M.

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