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This paper investigates the $$H_{\infty }$$ 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 $$H_{\infty }$$ 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. [ABSTRACT FROM AUTHOR]

The H filtering problem for two-dimensional Takagi-Sugeno fuzzy systems described by the Fornasini-Marchesini (FM) model is studied. Attention is focused on the design of an H fuzzy filter such that the filter error system is asymptotically stable and preserves a guaranteed H performance. By using basis-dependent Lyapunov functions and adding slack matrix variables, the coupling between the Lyapunov matrix and the system matrices is eliminated. Then, a linear matrix inequality (LMI)-based approach is developed for designing the H fuzzy filter. Finally, an illustrative example is provided to show the effectiveness of the proposed approach and less conservatism. [ABSTRACT FROM AUTHOR]