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

Abdelghani Djeddi, Djalel Dib, Ahmad Taher Azar and Salem Abdelmalek
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Abdelghani Djeddi: Department of Electrical Engineering, Larbi Tebessi University, Tebessa 12002, Algeria
Djalel Dib: Department of Electrical Engineering, Larbi Tebessi University, Tebessa 12002, Algeria
Ahmad Taher Azar: College of Engineering, Robotics and Internet-of-Things Lab (RIOTU), Prince Sultan University, Riyadh 12435, Saudi Arabia
Salem Abdelmalek: Department of Mathematics, Larbi Tebessi University, Tebessa 12002, Algeria

Mathematics, 2019, vol. 7, issue 10, 1-16

Abstract: 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.

Keywords: fractional order unknown input fuzzy observer; fractional order Takagi–Sugeno models; L 2 optimization; linear matrix inequalities; unmeasurable premise variables (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2019
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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