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. |
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). |