Fractional Order Unknown Inputs Fuzzy Observer for Takagi–Sugeno Systems with Unmeasurable Premise Variables
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 conside...
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| Format: | Article |
| Language: | English |
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MDPI AG
2019-10-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/7/10/984 |
| _version_ | 1811224769157136384 |
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| author | Abdelghani Djeddi Djalel Dib Ahmad Taher Azar Salem Abdelmalek |
| author_facet | Abdelghani Djeddi Djalel Dib Ahmad Taher Azar Salem Abdelmalek |
| author_sort | Abdelghani Djeddi |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-04-12T08:55:47Z |
| format | Article |
| id | doaj.art-2d5ccfdcd0d642dca4e10bc4f68e9097 |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-04-12T08:55:47Z |
| publishDate | 2019-10-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-2d5ccfdcd0d642dca4e10bc4f68e90972022-12-22T03:39:24ZengMDPI AGMathematics2227-73902019-10-0171098410.3390/math7100984math7100984Fractional Order Unknown Inputs Fuzzy Observer for Takagi–Sugeno Systems with Unmeasurable Premise VariablesAbdelghani Djeddi0Djalel Dib1Ahmad Taher Azar2Salem Abdelmalek3Department of Electrical Engineering, Larbi Tebessi University, Tebessa 12002, AlgeriaDepartment of Electrical Engineering, Larbi Tebessi University, Tebessa 12002, AlgeriaCollege of Engineering, Robotics and Internet-of-Things Lab (RIOTU), Prince Sultan University, Riyadh 12435, Saudi ArabiaDepartment of Mathematics, Larbi Tebessi University, Tebessa 12002, AlgeriaThis 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.https://www.mdpi.com/2227-7390/7/10/984fractional order unknown input fuzzy observerfractional order takagi–sugeno models<i>l<sub>2</sub></i> optimizationlinear matrix inequalitiesunmeasurable premise variables |
| spellingShingle | Abdelghani Djeddi Djalel Dib Ahmad Taher Azar Salem Abdelmalek Fractional Order Unknown Inputs Fuzzy Observer for Takagi–Sugeno Systems with Unmeasurable Premise Variables Mathematics fractional order unknown input fuzzy observer fractional order takagi–sugeno models <i>l<sub>2</sub></i> optimization linear matrix inequalities unmeasurable premise variables |
| title | Fractional Order Unknown Inputs Fuzzy Observer for Takagi–Sugeno Systems with Unmeasurable Premise Variables |
| title_full | Fractional Order Unknown Inputs Fuzzy Observer for Takagi–Sugeno Systems with Unmeasurable Premise Variables |
| title_fullStr | Fractional Order Unknown Inputs Fuzzy Observer for Takagi–Sugeno Systems with Unmeasurable Premise Variables |
| title_full_unstemmed | Fractional Order Unknown Inputs Fuzzy Observer for Takagi–Sugeno Systems with Unmeasurable Premise Variables |
| title_short | Fractional Order Unknown Inputs Fuzzy Observer for Takagi–Sugeno Systems with Unmeasurable Premise Variables |
| title_sort | fractional order unknown inputs fuzzy observer for takagi sugeno systems with unmeasurable premise variables |
| topic | fractional order unknown input fuzzy observer fractional order takagi–sugeno models <i>l<sub>2</sub></i> optimization linear matrix inequalities unmeasurable premise variables |
| url | https://www.mdpi.com/2227-7390/7/10/984 |
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