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In control theory, the robust properties of linear systems can be related directly to properties of the controllability or observability Gramian. In this paper, a discrete fuzzy controller for a class of nonlinear systems is developed to achieve a common controllability Gramian. We assume that the nonlinear system is represented by the Takagi‐Sugeno fuzzy model. The purpose of this paper is to find the output feedback gains for the T‐S fuzzy controller after assigning a certain common controllability Gramian. Finally, we provide a numerical example to verify the effects of the proposed method.

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This paper presents a new structure of Takagi-Sugeno (T-S) fuzzy controllers, which is called T-S fuzzy region controller or TSFRC for short. The fuzzy region concept is used to partition the plant rules into several fuzzy regions so that only one region is fired at the instant of each input vector being coming. Because each fuzzy region contains several plant rules, the fuzzy region can be regarded as a polytopic uncertain model. Therefore, robust control techniques would be essential for designing the feedback gains of each fuzzy region. To improve the speed of response, the decay rate constraint is imposed when deriving the stability conditions with Lyapunov stability criterion. To design TSFRC with the linear matrix inequality (LMI) solver, all stability conditions are represented in terms of LMIs. Finally, a two-link robot system is used to prove the feasibility and validity of the proposed method.