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

Salcedo, José V. ; Martínez, Miguel ; García-Nieto, Sergio ; Hilario, Adolfo

International Journal of Applied Mathematics and Computer Science, Tome 30 (2020) no. 3, pp. 529-550.

Résumé

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.

Détail

Keywords: linear matrix inequalities, Takagi–Suegno fuzzy system, fuzzy Lyapunov function, integral delayed Lyapunov function, nonparallel distributed fuzzy controller, generalised inescapable ellipsoids
Mots-clés : liniowe nierówności macierzowe, model rozmyty Takagi-Sugeno, funkcja Lapunowa

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