@ARTICLE{Almatroud_A._Othman_Different_2021,
 author={Almatroud, A. Othman and Ouannas, Adel and Grassi, Giuseppe and Batiha, Iqbal M. and Gasri, Ahlem and Al-Sawalha, M. Mossa},
 volume={vol. 31},
 number={No 4},
 journal={Archives of Control Sciences},
 pages={765-780},
 howpublished={online},
 year={2021},
 publisher={Committee of Automatic Control and Robotics PAS},
 abstract={Dynamics and control of discrete chaotic systems of fractional-order have received considerable attention over the last few years. So far, nonlinear control laws have been mainly used for stabilizing at zero the chaotic dynamics of fractional maps. This article provides a further contribution to such research field by presenting simple linear control laws for stabilizing three fractional chaotic maps in regard to their dynamics. Specifically, a one-dimensional linear control law and a scalar control law are proposed for stabilizing at the origin the chaotic dynamics of the Zeraoulia-Sprott rational map and the Ikeda map, respectively. Additionally, a two-dimensional linear control law is developed to stabilize the chaotic fractional flow map. All the results have been achieved by exploiting new theorems based on the Lyapunov method as well as on the properties of the Caputo h-difference operator. The relevant simulation findings are implemented to confirm the validity of the established linear control scheme.},
 type={Article},
 title={Different linear control laws for fractional chaotic maps using Lyapunov functional},
 URL={http://ochroma.man.poznan.pl/Content/121915/PDF-MASTER/art01.pdf},
 doi={10.24425/acs.2021.139729},
 keywords={discrete fractional calculus, chaotic maps, linear control, Lyapunov method},
}