2019
|
Yakoub, Zaineb; Amairi, Messaoud; Aoun, Mohamed; Chetoui, Manel On the fractional closed-loop linear parameter varying system identification under noise corrupted scheduling and output signal measurements Article de journal Dans: Transactions of the Institute of Measurement and Control, vol. 41, no. 10, p. 2909 – 2921, 2019, (Cited by: 3). @article{Yakoub20192909b,
title = {On the fractional closed-loop linear parameter varying system identification under noise corrupted scheduling and output signal measurements},
author = {Zaineb Yakoub and Messaoud Amairi and Mohamed Aoun and Manel Chetoui},
url = {https://www.scopus.com/inward/record.uri?eid=2-s2.0-85061267074\&doi=10.1177%2f0142331218821409\&partnerID=40\&md5=74b33d7ecf26b354ee27592a193b26d9},
doi = {10.1177/0142331218821409},
year = {2019},
date = {2019-01-01},
journal = {Transactions of the Institute of Measurement and Control},
volume = {41},
number = {10},
pages = {2909 \textendash 2921},
abstract = {It is well known that, in some industrial process identification situations, measurements can be collected from closed-loop experiments for several reasons such as stability, safety, and performance constraints. In this paper, we investigate the problem of identifying continuous-time fractional closed-loop linear parameter varying systems. The simplified refined instrumental variable method is developed to estimate both coefficients and differentiation orders. This method is established to provide consistent estimates when the output and the scheduling variable are contaminated by additive measurements noise. The proposed scheme is evaluated in comparison with other approaches in terms of a simulation example. © The Author(s) 2019.},
note = {Cited by: 3},
keywords = {Accident prevention, Calculations, Continuous time systems, Differentiation (calculus), Fractional calculus, Instrumental variables, Least Square, Linear parameters, Linear systems, Non-linear optimization, Nonlinear programming, Scheduling},
pubstate = {published},
tppubtype = {article}
}
It is well known that, in some industrial process identification situations, measurements can be collected from closed-loop experiments for several reasons such as stability, safety, and performance constraints. In this paper, we investigate the problem of identifying continuous-time fractional closed-loop linear parameter varying systems. The simplified refined instrumental variable method is developed to estimate both coefficients and differentiation orders. This method is established to provide consistent estimates when the output and the scheduling variable are contaminated by additive measurements noise. The proposed scheme is evaluated in comparison with other approaches in terms of a simulation example. © The Author(s) 2019. |
2014
|
Hmed, A. Ben; Amairi, M.; Najar, S.; Aoun, M. Resonance study of an elementary fractional transfer function of the third kind Conférence 2014, (Cited by: 3). @conference{BenHmed2014c,
title = {Resonance study of an elementary fractional transfer function of the third kind},
author = {A. Ben Hmed and M. Amairi and S. Najar and M. Aoun},
url = {https://www.scopus.com/inward/record.uri?eid=2-s2.0-84918559010\&doi=10.1109%2fICFDA.2014.6967437\&partnerID=40\&md5=51f3f51fd1030a736600ac71ffd6702d},
doi = {10.1109/ICFDA.2014.6967437},
year = {2014},
date = {2014-01-01},
journal = {2014 International Conference on Fractional Differentiation and Its Applications, ICFDA 2014},
abstract = {This work is devoted to the stability and resonance study of the elementary fractional transfer function of the third kind. Some basic properties of this transfer function which is written in the canonical form and characterized by a non commensurate order, a pseudo-damping factor and a natural frequency, are presented. A resonance and stability condition is established numerically in terms of the non commensurate order and the pseudo-damping factor. Many frequency-domain curves are given to determine graphically the pseudo-damping factor and the non commensurate order for a desired normalized gain and normalized resonant frequency. Illustrative examples are presented to show the correctness and the usefulness of these curves. © 2014 IEEE.},
note = {Cited by: 3},
keywords = {Calculations, Canonical form, Damping, Damping factors, Differentiation (calculus), Fractional calculus, Frequency domain analysis, Frequency domain curves, Frequency domains, Natural frequencies, Normalized gains, Resonance, Stability condition, Systems analysis, Transfer functions},
pubstate = {published},
tppubtype = {conference}
}
This work is devoted to the stability and resonance study of the elementary fractional transfer function of the third kind. Some basic properties of this transfer function which is written in the canonical form and characterized by a non commensurate order, a pseudo-damping factor and a natural frequency, are presented. A resonance and stability condition is established numerically in terms of the non commensurate order and the pseudo-damping factor. Many frequency-domain curves are given to determine graphically the pseudo-damping factor and the non commensurate order for a desired normalized gain and normalized resonant frequency. Illustrative examples are presented to show the correctness and the usefulness of these curves. © 2014 IEEE. |
Yakoub, Z.; Chetoui, M.; Amairi, M.; Aoun, M. Indirect approach for closed-loop system identification with fractional models Conférence 2014, (Cited by: 4). @conference{Yakoub2014c,
title = {Indirect approach for closed-loop system identification with fractional models},
author = {Z. Yakoub and M. Chetoui and M. Amairi and M. Aoun},
url = {https://www.scopus.com/inward/record.uri?eid=2-s2.0-84918521162\&doi=10.1109%2fICFDA.2014.6967441\&partnerID=40\&md5=d666e64f7fc6c6a967f8001f8f810bf2},
doi = {10.1109/ICFDA.2014.6967441},
year = {2014},
date = {2014-01-01},
journal = {2014 International Conference on Fractional Differentiation and Its Applications, ICFDA 2014},
abstract = {This paper deals with fractional closed-loop system identification using the indirect approach. Firstly, all differentiation orders are supposed known and only the coefficients of the closed-loop fractional transfer function are estimated using two methods based on least squares techniques. Then, the fractional open-loop process is determined by the knowledge of the regulator. A numerical example is presented to show the effectiveness of the proposed scheme. © 2014 IEEE.},
note = {Cited by: 4},
keywords = {Calculations, Closed loop systems, Closed loops, Differentiation (calculus), Fractional calculus, Fractional model, Identification (control systems), Least Square, Least squares approximations, Least squares techniques, Open-loop process, Religious buildings, State-variable filters},
pubstate = {published},
tppubtype = {conference}
}
This paper deals with fractional closed-loop system identification using the indirect approach. Firstly, all differentiation orders are supposed known and only the coefficients of the closed-loop fractional transfer function are estimated using two methods based on least squares techniques. Then, the fractional open-loop process is determined by the knowledge of the regulator. A numerical example is presented to show the effectiveness of the proposed scheme. © 2014 IEEE. |
Saidi, B.; Amairi, M.; Najar, S.; Aoun, M. Fractional PI design for time delay systems based on min-max optimization Conférence 2014, (Cited by: 7). @conference{Saidi2014d,
title = {Fractional PI design for time delay systems based on min-max optimization},
author = {B. Saidi and M. Amairi and S. Najar and M. Aoun},
url = {https://www.scopus.com/inward/record.uri?eid=2-s2.0-84918493100\&doi=10.1109%2fICFDA.2014.6967440\&partnerID=40\&md5=0ff2543768ac0713978d10873e94b207},
doi = {10.1109/ICFDA.2014.6967440},
year = {2014},
date = {2014-01-01},
journal = {2014 International Conference on Fractional Differentiation and Its Applications, ICFDA 2014},
abstract = {This paper presents a new design method of a fractional order PI (FO-PI) for time delay systems based on the min-max numerical optimization. The proposed method uses a constrained optimization algorithm to determine the unknown parameters of the controller and has an objective to improve the transient response, stability margin, stability robustness and load disturbance rejection. A simulation example is presented to show the effectiveness of the proposed design method for a First Order Plus Dead Time system (FOPDT). © 2014 IEEE.},
note = {Cited by: 7},
keywords = {Calculations, Constrained optimization, Delay control systems, Design, Differentiation (calculus), Disturbance rejection, First order plus dead time, Fractional calculus, Frequency specifications, Load disturbance rejection, Min-max optimization, Multiobjective optimization, Numerical methods, Numerical optimizations, Robust controllers, System stability, Time delay, Time-delay systems, Timing circuits, Transient analysis},
pubstate = {published},
tppubtype = {conference}
}
This paper presents a new design method of a fractional order PI (FO-PI) for time delay systems based on the min-max numerical optimization. The proposed method uses a constrained optimization algorithm to determine the unknown parameters of the controller and has an objective to improve the transient response, stability margin, stability robustness and load disturbance rejection. A simulation example is presented to show the effectiveness of the proposed design method for a First Order Plus Dead Time system (FOPDT). © 2014 IEEE. |
Hmed, A. Ben; Amairi, M.; Najar, S.; Aoun, M. Resonance study of an elementary fractional transfer function of the third kind Conférence 2014, (Cited by: 3). @conference{BenHmed2014e,
title = {Resonance study of an elementary fractional transfer function of the third kind},
author = {A. Ben Hmed and M. Amairi and S. Najar and M. Aoun},
url = {https://www.scopus.com/inward/record.uri?eid=2-s2.0-84918559010\&doi=10.1109%2fICFDA.2014.6967437\&partnerID=40\&md5=51f3f51fd1030a736600ac71ffd6702d},
doi = {10.1109/ICFDA.2014.6967437},
year = {2014},
date = {2014-01-01},
journal = {2014 International Conference on Fractional Differentiation and Its Applications, ICFDA 2014},
abstract = {This work is devoted to the stability and resonance study of the elementary fractional transfer function of the third kind. Some basic properties of this transfer function which is written in the canonical form and characterized by a non commensurate order, a pseudo-damping factor and a natural frequency, are presented. A resonance and stability condition is established numerically in terms of the non commensurate order and the pseudo-damping factor. Many frequency-domain curves are given to determine graphically the pseudo-damping factor and the non commensurate order for a desired normalized gain and normalized resonant frequency. Illustrative examples are presented to show the correctness and the usefulness of these curves. © 2014 IEEE.},
note = {Cited by: 3},
keywords = {Calculations, Canonical form, Damping, Damping factors, Differentiation (calculus), Fractional calculus, Frequency domain analysis, Frequency domain curves, Frequency domains, Natural frequencies, Normalized gains, Resonance, Stability condition, Systems analysis, Transfer functions},
pubstate = {published},
tppubtype = {conference}
}
This work is devoted to the stability and resonance study of the elementary fractional transfer function of the third kind. Some basic properties of this transfer function which is written in the canonical form and characterized by a non commensurate order, a pseudo-damping factor and a natural frequency, are presented. A resonance and stability condition is established numerically in terms of the non commensurate order and the pseudo-damping factor. Many frequency-domain curves are given to determine graphically the pseudo-damping factor and the non commensurate order for a desired normalized gain and normalized resonant frequency. Illustrative examples are presented to show the correctness and the usefulness of these curves. © 2014 IEEE. |
2011
|
Aoun, M.; Amairi, M.; Najar, S.; Abdelkrim, M. N. Simulation method of fractional systems based on the discrete-time approximation of the Caputo fractional derivatives Conférence 2011, (Cited by: 2). @conference{Aoun2011d,
title = {Simulation method of fractional systems based on the discrete-time approximation of the Caputo fractional derivatives},
author = {M. Aoun and M. Amairi and S. Najar and M. N. Abdelkrim},
url = {https://www.scopus.com/inward/record.uri?eid=2-s2.0-79957895222\&doi=10.1109%2fSSD.2011.5767414\&partnerID=40\&md5=21b4749453fc9c125b453521cfad3ec2},
doi = {10.1109/SSD.2011.5767414},
year = {2011},
date = {2011-01-01},
journal = {International Multi-Conference on Systems, Signals and Devices, SSD'11 - Summary Proceedings},
abstract = {This paper proposes a new method for the simulation of the fractional systems. It deals with the approximation methods of the fractional derivative. It compare the approximation based on Grnwald with Caputo approximation. The efficiency of each approximation methods in termes of execution time and quadratic error is evaluated for different differential orders and stepsize. The best approximation method is used to develop an original simulation method to demonstrate its effectiveness. © 2011 IEEE.},
note = {Cited by: 2},
keywords = {ACFDR, Approximation theory, CFDR, Diethelm's approximation, Differentiation (calculus), Fractional derivatives, Fractional systems, Pole-zero distribution, simulation},
pubstate = {published},
tppubtype = {conference}
}
This paper proposes a new method for the simulation of the fractional systems. It deals with the approximation methods of the fractional derivative. It compare the approximation based on Grnwald with Caputo approximation. The efficiency of each approximation methods in termes of execution time and quadratic error is evaluated for different differential orders and stepsize. The best approximation method is used to develop an original simulation method to demonstrate its effectiveness. © 2011 IEEE. |
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). @article{Malti20112425b,
title = {Analytical computation of the ℋ 2-norm of fractional commensurate transfer functions},
author = {Rachid Malti and Mohamed Aoun and Franois Levron and Alain Oustaloup},
url = {https://www.scopus.com/inward/record.uri?eid=2-s2.0-80053636175\&doi=10.1016%2fj.automatica.2011.08.021\&partnerID=40\&md5=6ef840171d4dc94041589e216e6aad44},
doi = {10.1016/j.automatica.2011.08.021},
year = {2011},
date = {2011-01-01},
journal = {Automatica},
volume = {47},
number = {11},
pages = {2425 \textendash 2432},
abstract = {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.},
note = {Cited by: 50},
keywords = {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},
pubstate = {published},
tppubtype = {article}
}
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). @article{Malti20112425,
title = {Analytical computation of the ℋ 2-norm of fractional commensurate transfer functions},
author = {Rachid Malti and Mohamed Aoun and Franois Levron and Alain Oustaloup},
url = {https://www.scopus.com/inward/record.uri?eid=2-s2.0-80053636175\&doi=10.1016%2fj.automatica.2011.08.021\&partnerID=40\&md5=6ef840171d4dc94041589e216e6aad44},
doi = {10.1016/j.automatica.2011.08.021},
year = {2011},
date = {2011-01-01},
journal = {Automatica},
volume = {47},
number = {11},
pages = {2425 \textendash 2432},
abstract = {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.},
note = {Cited by: 50},
keywords = {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},
pubstate = {published},
tppubtype = {article}
}
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
|
Aoun, Mohamed; Malti, Rachid; Levron, François; Oustaloup, Alain Numerical simulations of fractional systems Conférence vol. 5 A, 2003, (Cited by: 16). @conference{Aoun2003745b,
title = {Numerical simulations of fractional systems},
author = {Mohamed Aoun and Rachid Malti and Fran\c{c}ois Levron and Alain Oustaloup},
url = {https://www.scopus.com/inward/record.uri?eid=2-s2.0-1842734919\&doi=10.1115%2fdetc2003%2fvib-48389\&partnerID=40\&md5=fa18cbd478afa67e08d5de87422e273f},
doi = {10.1115/detc2003/vib-48389},
year = {2003},
date = {2003-01-01},
journal = {Proceedings of the ASME Design Engineering Technical Conference},
volume = {5 A},
pages = {745 \textendash 752},
abstract = {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.},
note = {Cited by: 16},
keywords = {Computer simulation, Differentiation (calculus), Fractional models, Fractional systems, Integration, Laplace transforms, Mathematical models, Transfer functions, Vectors},
pubstate = {published},
tppubtype = {conference}
}
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). @conference{Malti2003729b,
title = {H2 norm of fractional differential systems},
author = {Rachid Malti and Mohamed Aoun and Olivier Cois and Alain Oustaloup and Fran\c{c}ois Levron},
url = {https://www.scopus.com/inward/record.uri?eid=2-s2.0-1842634152\&doi=10.1115%2fdetc2003%2fvib-48387\&partnerID=40\&md5=0143c29ff9a0abd0533f228470954b52},
doi = {10.1115/detc2003/vib-48387},
year = {2003},
date = {2003-01-01},
journal = {Proceedings of the ASME Design Engineering Technical Conference},
volume = {5 A},
pages = {729 \textendash 735},
note = {Cited by: 19},
keywords = {Algebra, Computer simulation, Differential equations, Differentiation (calculus), Explicit systems, Fractional differential systems, Impulse response, Laplace transforms, Mathematical models, Theorem proving, Transfer functions},
pubstate = {published},
tppubtype = {conference}
}
|
Aoun, Mohamed; Malti, Rachid; Levron, François; Oustaloup, Alain Numerical simulations of fractional systems Conférence vol. 5 A, 2003, (Cited by: 16). @conference{Aoun2003745,
title = {Numerical simulations of fractional systems},
author = {Mohamed Aoun and Rachid Malti and Fran\c{c}ois Levron and Alain Oustaloup},
url = {https://www.scopus.com/inward/record.uri?eid=2-s2.0-1842734919\&doi=10.1115%2fdetc2003%2fvib-48389\&partnerID=40\&md5=fa18cbd478afa67e08d5de87422e273f},
doi = {10.1115/detc2003/vib-48389},
year = {2003},
date = {2003-01-01},
journal = {Proceedings of the ASME Design Engineering Technical Conference},
volume = {5 A},
pages = {745 \textendash 752},
abstract = {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.},
note = {Cited by: 16},
keywords = {Computer simulation, Differentiation (calculus), Fractional models, Fractional systems, Integration, Laplace transforms, Mathematical models, Transfer functions, Vectors},
pubstate = {published},
tppubtype = {conference}
}
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). @conference{Malti2003729,
title = {H2 norm of fractional differential systems},
author = {Rachid Malti and Mohamed Aoun and Olivier Cois and Alain Oustaloup and Fran\c{c}ois Levron},
url = {https://www.scopus.com/inward/record.uri?eid=2-s2.0-1842634152\&doi=10.1115%2fdetc2003%2fvib-48387\&partnerID=40\&md5=0143c29ff9a0abd0533f228470954b52},
doi = {10.1115/detc2003/vib-48387},
year = {2003},
date = {2003-01-01},
journal = {Proceedings of the ASME Design Engineering Technical Conference},
volume = {5 A},
pages = {729 \textendash 735},
note = {Cited by: 19},
keywords = {Algebra, Computer simulation, Differential equations, Differentiation (calculus), Explicit systems, Fractional differential systems, Impulse response, Laplace transforms, Mathematical models, Theorem proving, Transfer functions},
pubstate = {published},
tppubtype = {conference}
}
|
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). @conference{Malti2002449b,
title = {Energy of fractional order transfer functions},
author = {Rachid Malti and Olivier Cois and Mohammed Aoun and Fran\c{c}ois Levron and Alain Oustaloup},
url = {https://www.scopus.com/inward/record.uri?eid=2-s2.0-84945534478\&doi=10.3182%2f20020721-6-es-1901.00156\&partnerID=40\&md5=ec06924b792120270d919ea8a5620e72},
doi = {10.3182/20020721-6-es-1901.00156},
year = {2002},
date = {2002-01-01},
journal = {IFAC Proceedings Volumes (IFAC-PapersOnline)},
volume = {15},
number = {1},
pages = {449 \textendash 454},
abstract = {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.},
note = {Cited by: 5; All Open Access, Bronze Open Access},
keywords = {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},
pubstate = {published},
tppubtype = {conference}
}
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). @conference{Malti2002449,
title = {Energy of fractional order transfer functions},
author = {Rachid Malti and Olivier Cois and Mohammed Aoun and Fran\c{c}ois Levron and Alain Oustaloup},
url = {https://www.scopus.com/inward/record.uri?eid=2-s2.0-84945534478\&doi=10.3182%2f20020721-6-es-1901.00156\&partnerID=40\&md5=ec06924b792120270d919ea8a5620e72},
doi = {10.3182/20020721-6-es-1901.00156},
year = {2002},
date = {2002-01-01},
journal = {IFAC Proceedings Volumes (IFAC-PapersOnline)},
volume = {15},
number = {1},
pages = {449 \textendash 454},
abstract = {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.},
note = {Cited by: 5; All Open Access, Bronze Open Access},
keywords = {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},
pubstate = {published},
tppubtype = {conference}
}
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. |
