caa a22 4500 606205632 CHVBK 20210128101008.0 cr unu---uuuuu 210128e20150301xx s 000 0 eng 10.1007/s00034-014-9889-z doi (NATIONALLICENCE)springer-10.1007/s00034-014-9889-z $$H_{\infty }$$ H ∞ State Control for 2D Fuzzy FM Systems with Stochastic Perturbation [Elektronische Daten] [Bensalem Boukili, Abdelaziz Hmamed, Abdellah Benzaouia, Ahmed hajjaji] This paper investigates the $$H_{\infty }$$ H ∞ control problem for two-dimensional (2D) Takagi-Sugeno (T-S) fuzzy systems in a Fornasini-Marchesini second (FM II) model with stochastic perturbation. Our aim is to develop the state feedback control for 2D (T-S) fuzzy systems with stochastic perturbation and reduce the conservatism by using some slack matrices. Attention is focused on the design of the state feedback control, which guarantees the closed-loop system to be mean-square asymptotically stable and to have a prescribed $$H_{\infty }$$ H ∞ performance. Sufficient conditions are derived for the existence of such controls in terms of linear matrix inequalities, and the corresponding control synthesis problem, then, is solved. Numerical examples are given to demonstrate the effectiveness of the proposed method. Springer Science+Business Media New York, 2014 2D stochastic systems nationallicence 2D fuzzy systems nationallicence $$H_{\infty }$$ H ∞ performance nationallicence Stochastic perturbation nationallicence Robust control nationallicence Boukili Bensalem Faculty of Science Dhar El Mehraz, University Sidi Mohamed Ben Abdellah, B.P. 1796, Fez, Morocco aut Hmamed Abdelaziz Faculty of Science Dhar El Mehraz, University Sidi Mohamed Ben Abdellah, B.P. 1796, Fez, Morocco aut Benzaouia Abdellah LAEPT URAC 28, Faculty of Science Semlalia, University Cadi Ayyad, BP 2390, Marrakech, Morocco aut hajjaji Ahmed MIS Lab, UFR of Sciences, University of Picardie Jules-Vernes, 33 Rue St Leu, 80000, Amiens, France aut Circuits, Systems, and Signal Processing Springer US; http://www.springer-ny.com 34/3(2015-03-01), 779-796 0278-081X 34:3<779 2015 34 34 https://doi.org/10.1007/s00034-014-9889-z text/html Onlinezugriff via DOI BK010053 XK010053 XK010000 Metadata rights reserved Springer special CC-BY-NC licence nationallicence 1 research-article jats NATIONALLICENCE NATIONALLICENCE NL-springer NATIONALLICENCE 856 40 https://doi.org/10.1007/s00034-014-9889-z text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Boukili Bensalem Faculty of Science Dhar El Mehraz, University Sidi Mohamed Ben Abdellah, B.P. 1796, Fez, Morocco aut NATIONALLICENCE 700 1- Hmamed Abdelaziz Faculty of Science Dhar El Mehraz, University Sidi Mohamed Ben Abdellah, B.P. 1796, Fez, Morocco aut NATIONALLICENCE 700 1- Benzaouia Abdellah LAEPT URAC 28, Faculty of Science Semlalia, University Cadi Ayyad, BP 2390, Marrakech, Morocco aut NATIONALLICENCE 700 1- hajjaji Ahmed MIS Lab, UFR of Sciences, University of Picardie Jules-Vernes, 33 Rue St Leu, 80000, Amiens, France aut NATIONALLICENCE 773 0- Circuits, Systems, and Signal Processing Springer US; http://www.springer-ny.com 34/3(2015-03-01), 779-796 0278-081X 34:3<779 2015 34 34