$$H_{\infty }$$ H ∞ State Control for 2D Fuzzy FM Systems with Stochastic Perturbation

• DOI: 10.1007/s00034-014-9889-z
• Publication Date: 2014-09-15T11:38:28Z
• Authors: Bensalem Boukili; Abdelaziz Hmamed; Abdellah Benzaouia; Ahmed El hajjaji
• Keywords: 0209 industrial biotechnology; 02 engineering and technology

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.