Stabilization of Fractional-Order T–S Fuzzy Systems with Time Delays via an \(H_\infty\) Performance Model

Takagi–Sugeno (T–S) fuzzy model is an effective technology for describing complex nonlinear industrial processes and dynamic systems with unmeasurable parameters. However, to stabilize this type of system, feedback linearization techniques and complex adaptive schemes usually need to be adopted. This paper focuses on the stabilization of uncertain fractional-order (FO) systems with unmeasurable states, external disturbances, and time delays, where certain “IF-THEN” rules based on an FO T–S model are proposed to describe FO systems. A new FO \(H_\infty\) $H_{\infty }$ performance model is established to provide stabilization sufficient conditions. A fuzzy observer is implemented to reconstruct system states, and a feedback controller is established to stabilize the integrated system. Benefiting from a continuous frequency distribution model, the stabilization can be discussed through integer-order stabilization theories, and several stabilization conditions are obtained. Moreover, the proposed control approach avoids the usage of feedback linearization techniques, which effectively reduces the computational complexity. Apart from theoretical analysis, through a numerical experiment, the feasibility of derived results is verified.