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Robust functional observer for stabilising uncertain fuzzy systems with time-delay

  • Syed Imranul Islam
  • Peng Shi
  • Cheng-Chew Lim
Original Paper
  • 30 Downloads

Abstract

This paper presents a new technique for stabilising a Takagi–Sugeno (T-S) fuzzy system with time-delay and uncertainty. A robust fuzzy functional observer is employed to design a controller when the system states are not measurable. The model uncertainty is norm bounded, and the time-delay is time-varying but bounded. The parallel distributed compensation method is applied for defining the fuzzy functional observer to design this controller. The proposed procedure reduces the observer order to the dimension of the control input. Improved stability conditions are provided for the observer compared with the existing results of functional observer-based stabilisation of T-S fuzzy models. Lyapunov–Krasovskii functionals are used to construct delay-dependent stability conditions as linear matrix inequalities. The solution of these inequalities is used for calculating the observer parameters. The sensitivity of the estimation error to the model uncertainty is reduced by minimising the \(L_2\) gain. The new design method developed is illustrated and verified using two examples.

Keywords

Takagi–Sugeno fuzzy model Functional observer Time-delay Robust controller design 

Notes

Acknowledgements

This work was partially supported by the National Nature Science Foundation of China (61773131, U1509217), and the Australian Research Council (DP170102644).

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Copyright information

© Springer Nature Switzerland AG 2018

Authors and Affiliations

  1. 1.School of Electrical and Electronic EngineeringThe University of AdelaideAdelaideAustralia

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