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Article

Fractional Order Unknown Inputs Fuzzy Observer for Takagi–Sugeno Systems with Unmeasurable Premise Variables

by 1,†, 1,†, 2,3,*,† and 4,†
1
Department of Electrical Engineering, Larbi Tebessi University, Tebessa 12002, Algeria
2
College of Engineering, Robotics and Internet-of-Things Lab (RIOTU), Prince Sultan University, Riyadh 12435, Saudi Arabia
3
Faculty of Computers and Artificial Intelligence, Benha University, Benha 13511, Egypt
4
Department of Mathematics, Larbi Tebessi University, Tebessa 12002, Algeria
*
Author to whom correspondence should be addressed.
These authors contributed equally to this work.
Mathematics 2019, 7(10), 984; https://doi.org/10.3390/math7100984
Received: 21 August 2019 / Revised: 9 October 2019 / Accepted: 11 October 2019 / Published: 16 October 2019
This paper presents a new procedure for designing a fractional order unknown input observer (FOUIO) for nonlinear systems represented by a fractional-order Takagi–Sugeno (FOTS) model with unmeasurable premise variables (UPV). Most of the current research on fractional order systems considers models using measurable premise variables (MPV) and therefore cannot be utilized when premise variables are not measurable. The concept of the proposed is to model the FOTS with UPV into an uncertain FOTS model by presenting the estimated state in the model. First, the fractional-order extension of Lyapunov theory is used to investigate the convergence conditions of the FOUIO, and the linear matrix inequalities (LMIs) provide the stability condition. Secondly, performances of the proposed FOUIO are improved by the reduction of bounded external disturbances. Finally, an example is provided to clarify the proposed method. The obtained results show that a good convergence of the outputs and the state estimation errors were observed using the new proposed FOUIO. View Full-Text
Keywords: fractional order unknown input fuzzy observer; fractional order Takagi–Sugeno models; L2 optimization; linear matrix inequalities; unmeasurable premise variables fractional order unknown input fuzzy observer; fractional order Takagi–Sugeno models; L2 optimization; linear matrix inequalities; unmeasurable premise variables
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MDPI and ACS Style

Djeddi, A.; Dib, D.; Azar, A.T.; Abdelmalek, S. Fractional Order Unknown Inputs Fuzzy Observer for Takagi–Sugeno Systems with Unmeasurable Premise Variables. Mathematics 2019, 7, 984. https://doi.org/10.3390/math7100984

AMA Style

Djeddi A, Dib D, Azar AT, Abdelmalek S. Fractional Order Unknown Inputs Fuzzy Observer for Takagi–Sugeno Systems with Unmeasurable Premise Variables. Mathematics. 2019; 7(10):984. https://doi.org/10.3390/math7100984

Chicago/Turabian Style

Djeddi, Abdelghani, Djalel Dib, Ahmad Taher Azar, and Salem Abdelmalek. 2019. "Fractional Order Unknown Inputs Fuzzy Observer for Takagi–Sugeno Systems with Unmeasurable Premise Variables" Mathematics 7, no. 10: 984. https://doi.org/10.3390/math7100984

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