T–S Fuzzy Bibo Stabilisation of Non–Linear Systems Under Persistent Perturbations Using Fuzzy Lyapunov Functions and Non–PDC Control Laws

This paper develops an innovative approach for designing non-parallel distributed fuzzy controllers for continuous-time non-linear systems under persistent perturbations. Non-linear systems are represented using Takagi–Sugeno fuzzy models. These non-PDC controllers guarantee bounded input bounded ou...

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Vydáno v:International journal of applied mathematics and computer science Ročník 30; číslo 3; s. 529 - 550
Hlavní autoři: Salcedo, José V., Martínez, Miguel, García-Nieto, Sergio, Hilario, Adolfo
Médium: Journal Article
Jazyk:angličtina
Vydáno: Zielona Góra Sciendo 01.09.2020
De Gruyter Brill Sp. z o.o., Paradigm Publishing Services
Témata:
Controllers
Derivatives
Ellipsoids
Fuzzy control
fuzzy Lyapunov functions
generalised inescapable ellipsoids
integral delayed Lyapunov functions (IDLFs)
Integrals
Liapunov functions
Linear matrix inequalities
Linear systems
Mathematical analysis
non-parallel distributed fuzzy controllers (non-PDC)
Nonlinear control
Nonlinear systems
Takagi–Suegno fuzzy systems
Upper bounds
ISSN:1641-876X, 2083-8492
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Shrnutí:This paper develops an innovative approach for designing non-parallel distributed fuzzy controllers for continuous-time non-linear systems under persistent perturbations. Non-linear systems are represented using Takagi–Sugeno fuzzy models. These non-PDC controllers guarantee bounded input bounded output stabilisation in closed-loop throughout the computation of generalised inescapable ellipsoids. These controllers are computed with linear matrix inequalities using fuzzy Lyapunov functions and integral delayed Lyapunov functions. LMI conditions developed in this paper provide non-PDC controllers with a minimum *-norm (upper bound of the 1-norm) for the T–S fuzzy system under persistent perturbations. The results presented in this paper can be classified into two categories: local methods based on fuzzy Lyapunov functions with guaranteed bounds on the first derivatives of membership functions and global methods based on integral-delayed Lyapunov functions which are independent of the first derivatives of membership functions. The benefits of the proposed results are shown through some illustrative examples.
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ISSN:1641-876X
2083-8492
DOI:10.34768/amcs-2020-0039