A robust observer-based controller design for uncertain T–S fuzzy systems with unknown premise variables via LMI

This paper addresses the problem of robust H ∞ fuzzy observer-based controller design for the Takagi–Sugeno (T–S) fuzzy systems with unmeasurable premise variables. The proposed design method considers uncertainty for such a problem for the first time. Using some linear transformations for the output matrices of each local model of the T–S fuzzy system, and employing Finslerʹs lemma, the robust stability conditions in the form of linear matrix inequalities (LMIs) are derived. Two numerical simulations are provided to show the validity of the proposed method.