T–S fuzzy BIBO stabilisation of non-linear systems under persistent perturbations using fuzzy Lyapunov functions and non-PDC control laws

• Autorzy: Salcedo José V. , Martínez Miguel , García-Nieto Sergio , Hilario Adolfo

Identyfikatory

DOI

10.34768/amcs-2020-0039

• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

linear matrix inequalities; Takagi–Suegno fuzzy system; fuzzy Lyapunov function; integral delayed Lyapunov function; nonparallel distributed fuzzy controller; generalised inescapable ellipsoids

PL

liniowe nierówności macierzowe; model rozmyty Takagi-Sugeno; funkcja Lapunowa

• Wydawca: Oficyna Wydawnicza Uniwersytetu Zielonogórskiego
• Czasopismo: International Journal of Applied Mathematics and Computer Science
• Rocznik: 2020
• Tom: Vol. 30, no. 3
• Strony: 529--550
• Opis fizyczny: Bibliogr. 49 poz., rys., tab.

Twórcy

autor

Salcedo José V.

• Institute of Control Systems and Industrial Computing (ai2), Polytechnic University of Valencia, Camino de Vera S/N, 46022 Valencia, Spain

autor

Martínez Miguel

• Institute of Control Systems and Industrial Computing (ai2), Polytechnic University of Valencia, Camino de Vera S/N, 46022 Valencia, Spain

autor

García-Nieto Sergio

• Institute of Control Systems and Industrial Computing (ai2), Polytechnic University of Valencia, Camino de Vera S/N, 46022 Valencia, Spain

autor

Hilario Adolfo

• Institute of Control Systems and Industrial Computing (ai2), Polytechnic University of Valencia, Camino de Vera S/N, 46022 Valencia, Spain

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Uwagi

PL

Opracowanie rekordu ze środków MNiSW, umowa Nr 461252 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2020).