Abstract
The aim of this paper is to design an algebraic fractional order differentiator for a class of commensurate fractional order linear systems modeled by the pseudo-state space representation. For this purpose, a new algebraic method is introduced by designing an operator which can transform the considered system into a fractional order integral equation by eliminating unknown initial conditions. Based on the obtained equation, the desired fractional derivative is exactly given by a new algebraic formula using a recursive way. Then, a digital fractional order differentiator is introduced in discrete noisy cases. Finally, numerical results are given to illustrate the accuracy and the robustness of the proposed method.
Acknowledgements
This work was supported by the LE STUDIUM RESEARCH PROFESSORSHIP award of Centre Val de Loire region in France.
References
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© 2019 Diogenes Co., Sofia
Articles in the same Issue
- Frontmatter
- Editorial
- FCAA related news, events and books (FCAA–Volume 22–5–2019)
- Survey Paper
- A survey on fractional asymptotic expansion method: A forgotten theory
- Simplified fractional-order design of a MIMO robust controller
- Research Paper
- Embeddings of weighted generalized Morrey spaces into Lebesgue spaces on fractal sets
- Weyl integrals on weighted spaces
- On fractional regularity of distributions of functions in Gaussian random variables
- Compactness criteria for fractional integral operators
- Some results on the complete monotonicity of Mittag-Leffler functions of Le Roy type
- Method of upper and lower solutions for nonlinear Caputo fractional difference equations and its applications
- Numerical solution of fractional-order ordinary differential equations using the reformulated infinite state representation
- Supercritical fractional Kirchhoff type problems
- Identification for control of suspended objects in non-Newtonian fluids
- Algebraic fractional order differentiator based on the pseudo-state space representation
- Eigenvalues for a combination between local and nonlocal p-Laplacians
Articles in the same Issue
- Frontmatter
- Editorial
- FCAA related news, events and books (FCAA–Volume 22–5–2019)
- Survey Paper
- A survey on fractional asymptotic expansion method: A forgotten theory
- Simplified fractional-order design of a MIMO robust controller
- Research Paper
- Embeddings of weighted generalized Morrey spaces into Lebesgue spaces on fractal sets
- Weyl integrals on weighted spaces
- On fractional regularity of distributions of functions in Gaussian random variables
- Compactness criteria for fractional integral operators
- Some results on the complete monotonicity of Mittag-Leffler functions of Le Roy type
- Method of upper and lower solutions for nonlinear Caputo fractional difference equations and its applications
- Numerical solution of fractional-order ordinary differential equations using the reformulated infinite state representation
- Supercritical fractional Kirchhoff type problems
- Identification for control of suspended objects in non-Newtonian fluids
- Algebraic fractional order differentiator based on the pseudo-state space representation
- Eigenvalues for a combination between local and nonlocal p-Laplacians