<em>H</em><sub>∞</sub> and Passive Fuzzy Control for Non-Linear Descriptor Systems with Time-Varying Delay and Sensor Faults
In this paper, the problem of reliable control design with mixed <inline-formula><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><msub><mi>H</mi><mo>∞</mo></msub></semantics></math><...
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MDPI AG
2021-09-01
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| author | Houssem Jerbi Mourad Kchaou Attia Boudjemline Mohamed Amin Regaieg Sondes Ben Aoun Ahmed Lakhdar Kouzou |
| author_facet | Houssem Jerbi Mourad Kchaou Attia Boudjemline Mohamed Amin Regaieg Sondes Ben Aoun Ahmed Lakhdar Kouzou |
| author_sort | Houssem Jerbi |
| collection | DOAJ |
| description | In this paper, the problem of reliable control design with mixed <inline-formula><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><msub><mi>H</mi><mo>∞</mo></msub></semantics></math></inline-formula> /passive performance is discussed for a class of Takagi–Sugeno TS fuzzy descriptor systems with time-varying delay, sensor failure, and randomly occurred non-linearity. Based on the Lyapunov theory, firstly, a less conservative admissible criterion is established by combining the delay decomposition and reciprocally convex approaches. Then, the attention is focused on the design of a reliable static output feedback (SOF) controller with mixed <inline-formula><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><msub><mi>H</mi><mo>∞</mo></msub></semantics></math></inline-formula> /passive performance requirements. The key merit of the paper is to propose a simple method to design such a controller since the system output is subject to probabilistic missing data and noise. Using the output vector as a state component, an augmented model is introduced, and sufficient conditions are derived to achieve the desired performance of the closed-loop system. In addition, the cone complementarity linearization (CCL) algorithm is provided to calculate the controller gains. At last, three numerical examples, including computer-simulated truck-trailer and ball and beam systems are given to show the efficacy of our proposed approach, compared with existing ones in the literature. |
| first_indexed | 2024-03-10T07:28:21Z |
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| id | doaj.art-c3ffbe33e9f0485f8f5e094c85681ffe |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-10T07:28:21Z |
| publishDate | 2021-09-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-c3ffbe33e9f0485f8f5e094c85681ffe2023-11-22T14:04:50ZengMDPI AGMathematics2227-73902021-09-01918220310.3390/math9182203<em>H</em><sub>∞</sub> and Passive Fuzzy Control for Non-Linear Descriptor Systems with Time-Varying Delay and Sensor FaultsHoussem Jerbi0Mourad Kchaou1Attia Boudjemline2Mohamed Amin Regaieg3Sondes Ben Aoun4Ahmed Lakhdar Kouzou5Department of Industrial Engineering, College of Engineering, University of Hail, Hail 2440, Saudi ArabiaDepartment of Electrical Engineering, College of Engineering, University of Hail, Hail 2440, Saudi ArabiaDepartment of Industrial Engineering, College of Engineering, University of Hail, Hail 2440, Saudi ArabiaLab-STA, LR11ES50, National School of Engineering of Sfax, University of Sfax, Sfax 3038, TunisiaDepartment of Computer Engineering, College of Computer Science and Engineering, University of Hail, Hail 2440, Saudi ArabiaFaculty of Electrical and Control Engineering, Gdansk University of Technology, ul. Narutowicza 11/12, 80-233 Gdańsk, PolandIn this paper, the problem of reliable control design with mixed <inline-formula><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><msub><mi>H</mi><mo>∞</mo></msub></semantics></math></inline-formula> /passive performance is discussed for a class of Takagi–Sugeno TS fuzzy descriptor systems with time-varying delay, sensor failure, and randomly occurred non-linearity. Based on the Lyapunov theory, firstly, a less conservative admissible criterion is established by combining the delay decomposition and reciprocally convex approaches. Then, the attention is focused on the design of a reliable static output feedback (SOF) controller with mixed <inline-formula><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><msub><mi>H</mi><mo>∞</mo></msub></semantics></math></inline-formula> /passive performance requirements. The key merit of the paper is to propose a simple method to design such a controller since the system output is subject to probabilistic missing data and noise. Using the output vector as a state component, an augmented model is introduced, and sufficient conditions are derived to achieve the desired performance of the closed-loop system. In addition, the cone complementarity linearization (CCL) algorithm is provided to calculate the controller gains. At last, three numerical examples, including computer-simulated truck-trailer and ball and beam systems are given to show the efficacy of our proposed approach, compared with existing ones in the literature.https://www.mdpi.com/2227-7390/9/18/2203descriptor systemsTS fuzzy modelsensor failurerandomly occurred non-linearityCCL |
| spellingShingle | Houssem Jerbi Mourad Kchaou Attia Boudjemline Mohamed Amin Regaieg Sondes Ben Aoun Ahmed Lakhdar Kouzou <em>H</em><sub>∞</sub> and Passive Fuzzy Control for Non-Linear Descriptor Systems with Time-Varying Delay and Sensor Faults Mathematics descriptor systems TS fuzzy model sensor failure randomly occurred non-linearity CCL |
| title | <em>H</em><sub>∞</sub> and Passive Fuzzy Control for Non-Linear Descriptor Systems with Time-Varying Delay and Sensor Faults |
| title_full | <em>H</em><sub>∞</sub> and Passive Fuzzy Control for Non-Linear Descriptor Systems with Time-Varying Delay and Sensor Faults |
| title_fullStr | <em>H</em><sub>∞</sub> and Passive Fuzzy Control for Non-Linear Descriptor Systems with Time-Varying Delay and Sensor Faults |
| title_full_unstemmed | <em>H</em><sub>∞</sub> and Passive Fuzzy Control for Non-Linear Descriptor Systems with Time-Varying Delay and Sensor Faults |
| title_short | <em>H</em><sub>∞</sub> and Passive Fuzzy Control for Non-Linear Descriptor Systems with Time-Varying Delay and Sensor Faults |
| title_sort | em h em sub ∞ sub and passive fuzzy control for non linear descriptor systems with time varying delay and sensor faults |
| topic | descriptor systems TS fuzzy model sensor failure randomly occurred non-linearity CCL |
| url | https://www.mdpi.com/2227-7390/9/18/2203 |
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