Publications

@conference{Jerbi2022b,

title = {Computing the Domain of Attraction using Numerical Techniques},

author = {Houssem Jerbi and Boudour Dabbagui and Faical Hamidi and Mohamad Aoun and Yassine Bouazzi and Sondess Ben Aoun},

url = {https://www.scopus.com/inward/record.uri?eid=2-s2.0-85134079276\&doi=10.1109%2fICAAID51067.2022.9799499\&partnerID=40\&md5=74612f4dcc28a8c7f1c2bfe63a8c27d5},

doi = {10.1109/ICAAID51067.2022.9799499},

year  = {2022},

date = {2022-01-01},

journal = {Proceedings - 2022 4th International Conference on Applied Automation and Industrial Diagnostics, ICAAID 2022},

abstract = {Stability analysis of controlled nonlinear systems is a problem of fundamental importance in system engineering. This paper elaborates an explicit numerical technique to maximize a quadratic Lyapunov function for the class of polynomial nonlinear models. Using the computed Lyapunov function an enlarged subsets of the basin of attraction of an asymptotically stable equilibrium can be computed in an iterative analytical way. We mainly use the Carleman linearization technique that converts a nonlinear autonomous system of finite dimension into an equivalent linear infinite dimension one. We implement the sampling technique as a numerical tool allowing the maximization of estimated regions of attraction. An example is given to demonstrate the efficiency of the proposed approach. The numerical study analysis of the designed scheme is led using the Matlab software environment. © 2022 IEEE.},

note = {Cited by: 0},

keywords = {Asymptotically stable equilibrium, Basins of attraction, Carleman linearization, Domain of attraction, Iterative methods, Linearization, Lyapunov functions, Lyapunov's functions, Lypaunov functions, MATLAB, Non-linear modelling, Nonlinear systems, Numerical methods, Numerical techniques, Quadratic lyapunov function, Stability analyze, System stability},

pubstate = {published},

tppubtype = {conference}

}

@conference{Jerbi2022,

title = {Computing the Domain of Attraction using Numerical Techniques},

author = {Houssem Jerbi and Boudour Dabbagui and Faical Hamidi and Mohamad Aoun and Yassine Bouazzi and Sondess Ben Aoun},

url = {https://www.scopus.com/inward/record.uri?eid=2-s2.0-85134079276\&doi=10.1109%2fICAAID51067.2022.9799499\&partnerID=40\&md5=74612f4dcc28a8c7f1c2bfe63a8c27d5},

doi = {10.1109/ICAAID51067.2022.9799499},

year  = {2022},

date = {2022-01-01},

journal = {Proceedings - 2022 4th International Conference on Applied Automation and Industrial Diagnostics, ICAAID 2022},

abstract = {Stability analysis of controlled nonlinear systems is a problem of fundamental importance in system engineering. This paper elaborates an explicit numerical technique to maximize a quadratic Lyapunov function for the class of polynomial nonlinear models. Using the computed Lyapunov function an enlarged subsets of the basin of attraction of an asymptotically stable equilibrium can be computed in an iterative analytical way. We mainly use the Carleman linearization technique that converts a nonlinear autonomous system of finite dimension into an equivalent linear infinite dimension one. We implement the sampling technique as a numerical tool allowing the maximization of estimated regions of attraction. An example is given to demonstrate the efficiency of the proposed approach. The numerical study analysis of the designed scheme is led using the Matlab software environment. © 2022 IEEE.},

note = {Cited by: 0},

keywords = {Asymptotically stable equilibrium, Basins of attraction, Carleman linearization, Domain of attraction, Iterative methods, Linearization, Lyapunov functions, Lyapunov's functions, Lypaunov functions, MATLAB, Non-linear modelling, Nonlinear systems, Numerical methods, Numerical techniques, Quadratic lyapunov function, Stability analyze, System stability},

pubstate = {published},

tppubtype = {conference}

}

@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}

}

@conference{Malti2004835b,

title = {Synthesis of fractional Kautz-like basis with two periodically repeating complex conjugate modes},

author = {Rachid Malti and Mohamed Aoun and Alain Oustaloup},

url = {https://www.scopus.com/inward/record.uri?eid=2-s2.0-3042685548\&partnerID=40\&md5=957efcea75f0a5a34f4a77d45bd6e85c},

year  = {2004},

date = {2004-01-01},

journal = {International Symposium on Control, Communications and Signal Processing, ISCCSP},

pages = {835 \textendash 839},

abstract = {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.},

note = {Cited by: 19},

keywords = {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},

pubstate = {published},

tppubtype = {conference}

}

@conference{Malti2004835,

title = {Synthesis of fractional Kautz-like basis with two periodically repeating complex conjugate modes},

author = {Rachid Malti and Mohamed Aoun and Alain Oustaloup},

url = {https://www.scopus.com/inward/record.uri?eid=2-s2.0-3042685548\&partnerID=40\&md5=957efcea75f0a5a34f4a77d45bd6e85c},

year  = {2004},

date = {2004-01-01},

journal = {International Symposium on Control, Communications and Signal Processing, ISCCSP},

pages = {835 \textendash 839},

abstract = {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.},

note = {Cited by: 19},

keywords = {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},

pubstate = {published},

tppubtype = {conference}

}