Passive Fuzzy Controller Design for the Parameter-Dependent Polynomial Fuzzy Model

Cheung-Chieh Ku, Chein-Chung Sun (), Shao-Hao Jian and Wen-Jer Chang ()
Additional contact information
Cheung-Chieh Ku: Department of Marine Engineering, National Kaohsiung University of Science and Technology, Kaohsiung 805, Taiwan
Chein-Chung Sun: Department of Marine Engineering, National Kaohsiung University of Science and Technology, Kaohsiung 805, Taiwan
Shao-Hao Jian: Department of Marine Engineering, National Taiwan Ocean University, Keelung 202, Taiwan
Wen-Jer Chang: Department of Marine Engineering, National Taiwan Ocean University, Keelung 202, Taiwan

Mathematics, 2023, vol. 11, issue 11, 1-18

Abstract: This paper discusses a passive control issue for Nonlinear Time-Varying (NTV) systems subject to stability and attenuation performance. Based on the modeling approaches of Takagi-Sugeno (T-S) fuzzy model and Linear Parameter-Varying (LPV) model, a Parameter-Dependent Polynomial Fuzzy (PDPF) model is constructed to represent NTV systems. According to the Parallel Distributed Compensation (PDC) concept, a parameter-dependent polynomial fuzzy controller is built to achieve robust stability and passivity of the PDPF model. Furthermore, the passive theory is applied to achieve performance, constraining the disturbance effect on the PDPF systems. To develop the stability criteria, by introducing a parameter-dependent polynomial Lyapunov function, one can derive some stability conditions, which belong to the term of Sum-Of-Squares (SOS) form. Based on the Lyapunov function, two stability criteria are proposed to design the corresponding PDPF controller, such that the NTV system is robustly stable and passive. Finally, two examples are applied to demonstrate the effectiveness of the proposed stability criterion.

Keywords: T-S fuzzy system; LPV system; passive theory; SOS; parameter-dependent polynomial Lyapunov function (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
https://www.mdpi.com/2227-7390/11/11/2482/pdf (application/pdf)
https://www.mdpi.com/2227-7390/11/11/2482/ (text/html)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:gam:jmathe:v:11:y:2023:i:11:p:2482-:d:1157856

Access Statistics for this article

Mathematics is currently edited by Ms. Emma He

More articles in Mathematics from MDPI
Bibliographic data for series maintained by MDPI Indexing Manager ().