Non-quadratic exponential stabilisation of non-linear hyperbolic partial differential equation systems
In this study, a new systematic approach is proposed to design the fuzzy controller for a class of Takagi–Sugeno fuzzy-partial differential equation (TS fuzzy-PDE) systems which describe the non-linear distributed parameter system formulated by first-order semi-linear hyperbolic PDEs. In this study,...
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| Vydané v: | IET science, measurement & technology Ročník 8; číslo 6; s. 537 - 545 |
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| Jazyk: | English |
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The Institution of Engineering and Technology
01.11.2014
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| ISSN: | 1751-8822, 1751-8830 |
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| Abstract | In this study, a new systematic approach is proposed to design the fuzzy controller for a class of Takagi–Sugeno fuzzy-partial differential equation (TS fuzzy-PDE) systems which describe the non-linear distributed parameter system formulated by first-order semi-linear hyperbolic PDEs. In this study, non-quadratic Lyapunov function is utilised and some slack matrices are introduced to derive stability conditions in terms of linear matrix inequalities (LMIs). The proposed approach has three main features. First, stability conditions are not derived in the form of spatial differential LMI. Second, conservativeness of LMI conditions is reduced. Third, there is no restriction on the form of semi-linear hyperbolic PDE systems and therefore more semi-linear systems classes can be stabilised. Also, the proposed approach is more suitable for practical implementation compared with the recently published papers. |
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| AbstractList | In this study, a new systematic approach is proposed to design the fuzzy controller for a class of Takagi–Sugeno fuzzy-partial differential equation (TS fuzzy-PDE) systems which describe the non-linear distributed parameter system formulated by first-order semi-linear hyperbolic PDEs. In this study, non-quadratic Lyapunov function is utilised and some slack matrices are introduced to derive stability conditions in terms of linear matrix inequalities (LMIs). The proposed approach has three main features. First, stability conditions are not derived in the form of spatial differential LMI. Second, conservativeness of LMI conditions is reduced. Third, there is no restriction on the form of semi-linear hyperbolic PDE systems and therefore more semi-linear systems classes can be stabilised. Also, the proposed approach is more suitable for practical implementation compared with the recently published papers. |
| Author | Vafamand, Navid Babaei, Mohammad Sadegh Sha Sadeghi, Mokhtar |
| Author_xml | – sequence: 1 givenname: Mokhtar surname: Sha Sadeghi fullname: Sha Sadeghi, Mokhtar email: shasadeghi@sutech.ac.ir organization: 1Electrical and Electronics Department, Shiraz University of Technology, Shiraz, Iran – sequence: 2 givenname: Navid surname: Vafamand fullname: Vafamand, Navid organization: 1Electrical and Electronics Department, Shiraz University of Technology, Shiraz, Iran – sequence: 3 givenname: Mohammad Sadegh surname: Babaei fullname: Babaei, Mohammad Sadegh organization: 2E-Learning Department, Shiraz University, Shiraz, Iran |
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| CitedBy_id | crossref_primary_10_1080_23335777_2020_1837249 crossref_primary_10_1109_ACCESS_2018_2889650 crossref_primary_10_1115_1_4035240 crossref_primary_10_1002_rnc_5215 crossref_primary_10_1016_j_jfranklin_2016_04_021 crossref_primary_10_1109_TCYB_2019_2942685 crossref_primary_10_1016_j_isatra_2016_04_019 crossref_primary_10_1049_iet_cta_2017_0915 crossref_primary_10_1177_0959651815571621 crossref_primary_10_1016_j_engappai_2014_10_008 crossref_primary_10_1016_j_jfranklin_2017_07_025 crossref_primary_10_1109_TFUZZ_2017_2724018 crossref_primary_10_1109_TVT_2021_3091809 crossref_primary_10_1109_TFUZZ_2017_2688379 crossref_primary_10_1007_s12555_013_0497_7 crossref_primary_10_1002_asjc_1429 crossref_primary_10_1016_j_engappai_2016_09_002 |
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| Keywords | hyperbolic equations fuzzy controller design first order semilinear hyperbolic PDE nonlinear distributed parameter system nonquadratic Lyapunov function nonlinear hyperbolic partial differential equation systems control system synthesis LMI asymptotic stability stability conditions nonlinear differential equations fuzzy control linear matrix inequalities nonlinear control systems nonquadratic exponential stabilisation distributed parameter systems partial differential equations TS fuzzy-PDE system systematic approach Lyapunov methods Takagi–Sugeno fuzzy partial differential equation |
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| Snippet | In this study, a new systematic approach is proposed to design the fuzzy controller for a class of Takagi–Sugeno fuzzy-partial differential equation (TS... In this study, a new systematic approach is proposed to design the fuzzy controller for a class of Takagi–Sugeno fuzzy‐partial differential equation (TS... In this study, a new systematic approach is proposed to design the fuzzy controller for a class of Takagi-Sugeno fuzzy-partial differential equation (TS... |
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| SubjectTerms | asymptotic stability control system synthesis Design engineering Design parameters Differential equations distributed parameter systems first order semilinear hyperbolic PDE Fuzzy control fuzzy controller design hyperbolic equations linear matrix inequalities LMI Lyapunov functions Lyapunov methods nonlinear control systems nonlinear differential equations nonlinear distributed parameter system nonlinear hyperbolic partial differential equation systems Nonlinearity nonquadratic exponential stabilisation nonquadratic Lyapunov function Partial differential equations Stability stability conditions systematic approach Takagi–Sugeno fuzzy partial differential equation TS fuzzy‐PDE system |
| Title | Non-quadratic exponential stabilisation of non-linear hyperbolic partial differential equation systems |
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