2004 |
Aoun, Mohamed; Malti, Rachid; Levron, François; Oustaloup, Alain Numerical simulations of fractional systems: An overview of existing methods and improvements Article de journal Dans: Nonlinear Dynamics, vol. 38, no. 1-4, p. 117 – 131, 2004, (Cited by: 117). Résumé | Liens | BibTeX | Étiquettes: Approximation theory, Computer simulation, Continuous time model, Differential equations, Discrete time model, Fractional calculus, Fractional model, Functions, Identification (control systems), Laplace transforms, Mathematical models, Time domain analysis @article{Aoun2004117b,An overview of the main simulation methods of fractional systems is presented. Based on Oustaloup’s recursive poles and zeros approximation of a fractional integrator in a frequency band some improvements are proposed. They take into account boundary effects around outer frequency limits and simplify the synthesis of a rational approximation by eliminating arbitrarily chosen parameters. © 2004 Kluwer Academic Publishers. |
Malti, Rachid; Aoun, Mohamed; Oustaloup, Alain Synthesis of fractional Kautz-like basis with two periodically repeating complex conjugate modes Conférence 2004, (Cited by: 19). Résumé | Liens | BibTeX | Étiquettes: Approximation theory, Differential equations, Dynamical systems, Extrapolation, Fractional calculus, Fractional derivatives, Generalized orthogonal basis (GOB), Identification (control systems), Laplace transforms, Linear control systems, Mathematical models, Model reduction, Orthogonal functions, Polynomials, Set theory, System stability, Transfer functions @conference{Malti2004835b,Fractional Kautz-like functions are synthesized extrapolating the definition of classical Kautz functions to fractional derivatives. The synthesized bases has two periodically repeating complex conjugate modes. The new basis extends the definition of the fractional Laguerre basis, by allowing the modes to be complex. An example is then provided in system identification context. |
Aoun, Mohamed; Malti, Rachid; Levron, François; Oustaloup, Alain Numerical simulations of fractional systems: An overview of existing methods and improvements Article de journal Dans: Nonlinear Dynamics, vol. 38, no. 1-4, p. 117 – 131, 2004, (Cited by: 117). Résumé | Liens | BibTeX | Étiquettes: Approximation theory, Computer simulation, Continuous time model, Differential equations, Discrete time model, Fractional calculus, Fractional model, Functions, Identification (control systems), Laplace transforms, Mathematical models, Time domain analysis @article{Aoun2004117,An overview of the main simulation methods of fractional systems is presented. Based on Oustaloup’s recursive poles and zeros approximation of a fractional integrator in a frequency band some improvements are proposed. They take into account boundary effects around outer frequency limits and simplify the synthesis of a rational approximation by eliminating arbitrarily chosen parameters. © 2004 Kluwer Academic Publishers. |
Malti, Rachid; Aoun, Mohamed; Oustaloup, Alain Synthesis of fractional Kautz-like basis with two periodically repeating complex conjugate modes Conférence 2004, (Cited by: 19). Résumé | Liens | BibTeX | Étiquettes: Approximation theory, Differential equations, Dynamical systems, Extrapolation, Fractional calculus, Fractional derivatives, Generalized orthogonal basis (GOB), Identification (control systems), Laplace transforms, Linear control systems, Mathematical models, Model reduction, Orthogonal functions, Polynomials, Set theory, System stability, Transfer functions @conference{Malti2004835,Fractional Kautz-like functions are synthesized extrapolating the definition of classical Kautz functions to fractional derivatives. The synthesized bases has two periodically repeating complex conjugate modes. The new basis extends the definition of the fractional Laguerre basis, by allowing the modes to be complex. An example is then provided in system identification context. |
2003 |
Aoun, Mohamed; Malti, Rachid; Levron, François; Oustaloup, Alain Numerical simulations of fractional systems Conférence vol. 5 A, 2003, (Cited by: 16). Résumé | Liens | BibTeX | Étiquettes: Computer simulation, Differentiation (calculus), Fractional models, Fractional systems, Integration, Laplace transforms, Mathematical models, Transfer functions, Vectors @conference{Aoun2003745b,This paper deals with the design and simulation of continuous-time models with fractional differentiation orders. Two new methods are proposed. The first is an improvement of the approximation of the fractional integration operator using recursive poles and zeros proposed by Oustaloup (1995) and Lin (2001). The second improves the simulation schema by using a modal representation. |
Malti, Rachid; Aoun, Mohamed; Cois, Olivier; Oustaloup, Alain; Levron, François H2 norm of fractional differential systems Conférence vol. 5 A, 2003, (Cited by: 19). Liens | BibTeX | Étiquettes: Algebra, Computer simulation, Differential equations, Differentiation (calculus), Explicit systems, Fractional differential systems, Impulse response, Laplace transforms, Mathematical models, Theorem proving, Transfer functions @conference{Malti2003729b, |
Aoun, Mohamed; Malti, Rachid; Levron, François; Oustaloup, Alain Numerical simulations of fractional systems Conférence vol. 5 A, 2003, (Cited by: 16). Résumé | Liens | BibTeX | Étiquettes: Computer simulation, Differentiation (calculus), Fractional models, Fractional systems, Integration, Laplace transforms, Mathematical models, Transfer functions, Vectors @conference{Aoun2003745,This paper deals with the design and simulation of continuous-time models with fractional differentiation orders. Two new methods are proposed. The first is an improvement of the approximation of the fractional integration operator using recursive poles and zeros proposed by Oustaloup (1995) and Lin (2001). The second improves the simulation schema by using a modal representation. |
Malti, Rachid; Aoun, Mohamed; Cois, Olivier; Oustaloup, Alain; Levron, François H2 norm of fractional differential systems Conférence vol. 5 A, 2003, (Cited by: 19). Liens | BibTeX | Étiquettes: Algebra, Computer simulation, Differential equations, Differentiation (calculus), Explicit systems, Fractional differential systems, Impulse response, Laplace transforms, Mathematical models, Theorem proving, Transfer functions @conference{Malti2003729, |
Publications
2004 |
Numerical simulations of fractional systems: An overview of existing methods and improvements Article de journal Dans: Nonlinear Dynamics, vol. 38, no. 1-4, p. 117 – 131, 2004, (Cited by: 117). |
Synthesis of fractional Kautz-like basis with two periodically repeating complex conjugate modes Conférence 2004, (Cited by: 19). |
Numerical simulations of fractional systems: An overview of existing methods and improvements Article de journal Dans: Nonlinear Dynamics, vol. 38, no. 1-4, p. 117 – 131, 2004, (Cited by: 117). |
Synthesis of fractional Kautz-like basis with two periodically repeating complex conjugate modes Conférence 2004, (Cited by: 19). |
2003 |
Numerical simulations of fractional systems Conférence vol. 5 A, 2003, (Cited by: 16). |
H2 norm of fractional differential systems Conférence vol. 5 A, 2003, (Cited by: 19). |
Numerical simulations of fractional systems Conférence vol. 5 A, 2003, (Cited by: 16). |
H2 norm of fractional differential systems Conférence vol. 5 A, 2003, (Cited by: 19). |