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Paper details
Number 3 - September 2020
Volume 30 - 2020
T–S fuzzy BIBO stabilisation of non-linear systems under persistent perturbations using fuzzy Lyapunov functions and non-PDC control laws
José V. Salcedo, Miguel Martínez, Sergio García-Nieto, Adolfo Hilario
Abstract
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.
Keywords
linear matrix inequalities, Takagi–Suegno fuzzy systems, fuzzy Lyapunov functions, integral delayed Lyapunov functions (IDLFs), non-parallel distributed fuzzy controllers (non-PDC), generalised inescapable ellipsoids