2011 |
Malti, Rachid; Aoun, Mohamed; Levron, Franois; Oustaloup, Alain Analytical computation of the ℋ 2-norm of fractional commensurate transfer functions Article de journal Dans: Automatica, vol. 47, no. 11, p. 2425 – 2432, 2011, (Cited by: 50). Résumé | Liens | BibTeX | Étiquettes: Analytical computations, Closed loop control systems, Differentiation (calculus), Finiteness condition, Fractional calculus, Function coefficients, General expression, Impulse response, Impulse response energy, Integral squared error, Performance indices, Rational functions, Rational transfer functions, Relative degrees, Three term control systems, Transfer functions @article{Malti20112425b,ℋ2-norm, or impulse response energy, of any fractional commensurate transfer function is computed analytically. A general expression depending on transfer function coefficients and differentiation orders is established. Then, more concise expressions are given for elementary fractional transfer functions. Unlike stable rational transfer functions, it is proven that the ℋ2-norm of stable fractional transfer functions may be infinite. Finiteness conditions are established in terms of transfer function relative degree. Moreover, it is proven that the ℋ2-norm of a fractional transfer function with a proper integrator of order less than 0.5 may be finite. The obtained results are used to evaluate the integral squared error of closed-loop control systems. © 2011 Elsevier Ltd. All rights reserved. |
Malti, Rachid; Aoun, Mohamed; Levron, Franois; Oustaloup, Alain Analytical computation of the ℋ 2-norm of fractional commensurate transfer functions Article de journal Dans: Automatica, vol. 47, no. 11, p. 2425 – 2432, 2011, (Cited by: 50). Résumé | Liens | BibTeX | Étiquettes: Analytical computations, Closed loop control systems, Differentiation (calculus), Finiteness condition, Fractional calculus, Function coefficients, General expression, Impulse response, Impulse response energy, Integral squared error, Performance indices, Rational functions, Rational transfer functions, Relative degrees, Three term control systems, Transfer functions @article{Malti20112425,ℋ2-norm, or impulse response energy, of any fractional commensurate transfer function is computed analytically. A general expression depending on transfer function coefficients and differentiation orders is established. Then, more concise expressions are given for elementary fractional transfer functions. Unlike stable rational transfer functions, it is proven that the ℋ2-norm of stable fractional transfer functions may be infinite. Finiteness conditions are established in terms of transfer function relative degree. Moreover, it is proven that the ℋ2-norm of a fractional transfer function with a proper integrator of order less than 0.5 may be finite. The obtained results are used to evaluate the integral squared error of closed-loop control systems. © 2011 Elsevier Ltd. All rights reserved. |
2003 |
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, |
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, |
2002 |
Malti, Rachid; Cois, Olivier; Aoun, Mohammed; Levron, François; Oustaloup, Alain Energy of fractional order transfer functions Conférence vol. 15, no. 1, 2002, (Cited by: 5; All Open Access, Bronze Open Access). Résumé | Liens | BibTeX | Étiquettes: Automation, Calculations, Differentiation (calculus), Dynamical systems, Fractional calculus, Fractional order differentiations, Fractional order transfer function, Impulse response, Impulse response energy, Lebesgue space, Single mode, Square integrable, Strictly positive real, Transfer functions @conference{Malti2002449b,The objective of the paper is to compute the impulse response energy of a fractional order transfer function having a single mode. The differentiation order n, defined in the sense of Riemann-Liouville, is allowed to be a strictly positive real number. A necessary and sufficient condition is established on n, in order for the impulse response to belong to the Lebesgue space L2[0, ∞[ of square integrable functions on [0, ∞[. Copyright © 2002 IFAC. |
Malti, Rachid; Cois, Olivier; Aoun, Mohammed; Levron, François; Oustaloup, Alain Energy of fractional order transfer functions Conférence vol. 15, no. 1, 2002, (Cited by: 5; All Open Access, Bronze Open Access). Résumé | Liens | BibTeX | Étiquettes: Automation, Calculations, Differentiation (calculus), Dynamical systems, Fractional calculus, Fractional order differentiations, Fractional order transfer function, Impulse response, Impulse response energy, Lebesgue space, Single mode, Square integrable, Strictly positive real, Transfer functions @conference{Malti2002449,The objective of the paper is to compute the impulse response energy of a fractional order transfer function having a single mode. The differentiation order n, defined in the sense of Riemann-Liouville, is allowed to be a strictly positive real number. A necessary and sufficient condition is established on n, in order for the impulse response to belong to the Lebesgue space L2[0, ∞[ of square integrable functions on [0, ∞[. Copyright © 2002 IFAC. |
Publications
2011 |
Analytical computation of the ℋ 2-norm of fractional commensurate transfer functions Article de journal Dans: Automatica, vol. 47, no. 11, p. 2425 – 2432, 2011, (Cited by: 50). |
Analytical computation of the ℋ 2-norm of fractional commensurate transfer functions Article de journal Dans: Automatica, vol. 47, no. 11, p. 2425 – 2432, 2011, (Cited by: 50). |
2003 |
H2 norm of fractional differential systems Conférence vol. 5 A, 2003, (Cited by: 19). |
H2 norm of fractional differential systems Conférence vol. 5 A, 2003, (Cited by: 19). |
2002 |
Energy of fractional order transfer functions Conférence vol. 15, no. 1, 2002, (Cited by: 5; All Open Access, Bronze Open Access). |
Energy of fractional order transfer functions Conférence vol. 15, no. 1, 2002, (Cited by: 5; All Open Access, Bronze Open Access). |