T-S Fuzzy H∞Observer-Controller Design for 2-D Systems

The paper investigates the design problem of fuzzy observer-based H∞ control for two-dimensional 2-D discrete-time Takagi-Sugeno (T-S) fuzzy systems described by the second Fornasini-Marchesini F-M model. The use of fuzzy Lyapunov functions and free-weighting matrices allows to implement a new design process. Then, using certain particular derivations, Bi-linear Matrix Inequalities (BMIs) are successfully turned into a set of Linear Matrix Inequalities (LMIs) that can be solved in a single step. Then, the presented method allows simultaneously computing the fuzzy observer and controller gains, with a prescribed H∞ noise attenuation γ for the whole system. Finally, a practical example is provided to verify the effectiveness and applicability of the proposed observer-based fuzzy control approach. © 2022 IEEE.