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Proportional Plus Derivative State Feedback Control of Takagi-Sugeno Fuzzy Singular Fractional Order Systems

Xuefeng Zhang* and Kaijing Jin
International Journal of Control, Automation, and Systems, vol. 19, no. 11, pp.3823-3829, 2021

Abstract : This paper investigates the fuzzy normalization and stabilization issues of a class of singular fractional order nonlinear systems with order 0 < α < 1 based on a singular Takagi-Sugeno fuzzy model. First, we present the admissibility theorem of Takagi-Sugeno fuzzy singular fractional order systems. Next, benefited by that the fuzzy model and the state feedback controllers do not share the same membership functions, a proportional plus derivative state feedback controller is designed, which guarantees the closed-loop system normalized and admissible. Finally, a numerical simulation example is given to illustrate the effectiveness of the proposed method.

Keyword : Admissibility, fractional order systems, singular systems, Takagi-Sugeno fuzzy systems

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