Enlarging the Domain of Attraction in Nonlinear Polynomial Systems
AbstractThis paper addresses the problem of enlarging the Domain of Attraction (DA) based on a Generalized Eigenvalue Problem (GEVP) approach. The main contribution of the present development is the maximization of the (DA) while characterizing the asymptotic stability region by a Lyapunov Function. Such result is obtained using a Genetic Algorithm (GA) . A theoretical proof of the validity of the obtained domain is developed. An illustrative example ends the paper.
 F. Hamidi, H. Jerbi, W. Aggoune, M. Djema and M. Naceur Abdkrim, Enlarging region of attraction via LMI-based approach and Genetic Algorithm. 1st Int. Conf. on Communications, Computing and Control Applications, Hammamet Tunisia 2011.
 G. Chesi, Computing output feedback controllers to enlarge the domain of attraction in polynomial systems. IEEE Trans. on Automatic Control, vol. 49, pp 1846-1850, 2004.
 G. Chesi, A. Garulli, A. Tesi and A. Vicino. Characterizing the solution set of polynomial systems in terms of homogeneous forms: an LMI approach. Int. J. of Nonlinear and Robust Control, Vol. 13(13), pp 1239-1257, 2003.
 G. Chesi, A. Garulli, A. Tesi and A. Vicino. Solving quadratic distance problems: an LMI approach. IEEE Transactions on Automatic Control, vol. 13, pp 200-212, 2003.
 G. Chesi, A. Garulli, A. Tesi and A. Vicino. Homogeneous Lyapunov function for systems with structured uncertainties. Automatica, vol.39, no. 6, pp. 1027-1035, 2003.
 H.K. Khalil, Nonlinear systems, in Third Edition Upper Saddle River, NJ :Prentice Hall, 2001.
 M. Loccuer and E. Noldus. A new trajectory Reversing Method for Estimating Stability Regions of autonomous Nonlinear Systems. Nonlinear dynamics 21, pp. 265-288, 2000.
 M. Loccuer and E. Noldus. On the estimation of asymptotic stability regions for au- tonomous nonlinear systems. IMA Journal of Mathematic Control an Information 12, pp. 91-109, 1995.
 M.M. Belhaouane, R. Mtar, H. Belkhiria Ayadi and N. Benhadj Braiek. An LMI Tech- nique for the Global Stabilization of Nonlinear Polynomial Systems. International Journal of Computers, Communications and Control (IJCCC), 4(4):335-348, 2009.
 O. Hachido, and B. Tibken. Estimating domains of attractions of a class of nonlinear dynamical systems with LMI methods based on the theory of moments. Proceedings of the 41st IEEE Conference on Decision and Control, Las Vegas, Nevada, pp 3150-3155, 2002.
 R. Genesio, M. Tartaglia and A. Vicino. On the estimation of asymptotic stability regions: state of the art and new proposals. IEEE Transactions on Automatic Control, vol. AC 30, no. 8, pp 747-755, 1985.
 Y. Fujisaki, and R. Sakuwa. Estimation of asymptotic stability regions via homogeneous polynomial Lyapunov functions. International Journal of Control, vol. 79, no. 6, pp. 617- 623, 2006.
This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.
ONLINE OPEN ACCES: Acces to full text of each article and each issue are allowed for free in respect of Attribution-NonCommercial 4.0 International (CC BY-NC 4.0.
You are free to:
-Share: copy and redistribute the material in any medium or format;
-Adapt: remix, transform, and build upon the material.
The licensor cannot revoke these freedoms as long as you follow the license terms.
DISCLAIMER: The author(s) of each article appearing in International Journal of Computers Communications & Control is/are solely responsible for the content thereof; the publication of an article shall not constitute or be deemed to constitute any representation by the Editors or Agora University Press that the data presented therein are original, correct or sufficient to support the conclusions reached or that the experiment design or methodology is adequate.