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T-S Fuzzy Control of Uncertain Fractional-Order Systems with Time Delay

Author

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  • Yilin Hao
  • Xiulan Zhang
  • Shenggang Li

Abstract

In this article, the adaptive control of uncertain fractional-order time-delay systems (FOTDSs) with external disturbances is discussed. A Takagi-Sugenu (T-S) fuzzy model with if-then rules is adopted to characterize the dynamic equation of the FOTDS. Besides, a fuzzy adaptive method is proposed to stabilize the model. By utilizing the Lyapunov functions, a robust controller is constructed to stabilize the FOTDS. Due to the uncertainty of system parameters, some fractional-order adaptation laws are designed to update these parameters. At the same time, some if-then rules with linear structure based on the fuzzy T-S adaption concept are established. The designed method not only guarantees that the state of closed-loop system asymptotically converges to origin but also keeps the signal in the FOTDS bounded. Finally, the applicability of the control method is proved by simulation examples.

Suggested Citation

  • Yilin Hao & Xiulan Zhang & Shenggang Li, 2021. "T-S Fuzzy Control of Uncertain Fractional-Order Systems with Time Delay," Journal of Mathematics, Hindawi, vol. 2021, pages 1-9, January.
    • Handle: RePEc:hin:jjmath:6636882
    DOI: 10.1155/2021/6636882
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