State/Disturbance Observer and Controller Synthesis for the T–S Fuzzy System With an Enlarged Class of Disturbances

This paper proposes a novel approach for designing the observer and controller for Takagi–Sugeno (T–S) fuzzy systems with an enlarged class of disturbances. The class of the disturbances in this study is significantly enlarged because they do not need to satisfy the constraints such as bounded, generated from an exogenous system, or finite derivative is equal to zero. First, the state/disturbance observer is proposed to estimate the unmeasurable states and disturbances, simultaneously. Then, the controller incorporating with the observer is synthesized to attenuate the disturbances completely and stabilize the T–S fuzzy systems. On the basis of the Lyapunov function and linear matrix inequality technique, the sufficient conditions for the synthesis of the observer and controller are derived in the main theorems. Finally, the effectiveness of the proposed method is verified via two examples.

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