<abstract xmlns="http://www.w3.org/1999/xhtml"><p>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.</p></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.

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

International Journal of Applied Mathematics and Computer Science

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

This paper develops an innovative approach for designing non-parallel distributed fuzzy controllers for continuous-time non-linear systems under persistent...

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

Published Online: Sep 29, 2020

Page range: 529 - 550

Received: Jan 01, 2020

Accepted: May 25, 2020

DOI: https://doi.org/10.34768/amcs-2020-0039

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

© 2020 José V. Salcedo et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

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

Published Online: Sep 29, 2020

Page range: 529 - 550

Received: Jan 01, 2020

Accepted: May 25, 2020

DOI: https://doi.org/10.34768/amcs-2020-0039

Keywordslinear matrix inequalities, Takagi–Suegno fuzzy systems, fuzzy Lyapunov functions, integral delayed Lyapunov functions (IDLFs), non-parallel distributed fuzzy controllers (non-PDC), generalised inescapable ellipsoids

© 2020 José V. Salcedo et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

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