<abstract xmlns="http://www.w3.org/1999/xhtml">This paper presents a novel approach to the design of fuzzy state feedback controllers for continuous-time non-linear systems with input saturation under persistent perturbations. It is assumed that all the states of the Takagi-Sugeno (TS) fuzzy model representing a non-linear system are measurable. Such controllers achieve bounded input bounded output (BIBO) stabilisation in closed loop based on the computation of inescapable ellipsoids. These ellipsoids are computed with linear matrix inequalities (LMIs) that guarantee stabilisation with input saturation and persistent perturbations. In particular, two kinds of inescapable ellipsoids are computed when solving a multiobjective optimization problem: the maximum volume inescapable ellipsoids contained inside the validity domain of the TS fuzzy model and the smallest inescapable ellipsoids which guarantee a minimum *-norm (upper bound of the 1-norm) of the perturbed system. For every initial point contained in the maximum volume ellipsoid, the closed loop will enter the minimum *-norm ellipsoid after a finite time, and it will remain inside afterwards. Consequently, the designed controllers have a large domain of validity and ensure a small value for the 1-norm of closed loop.</abstract>

This paper presents a novel approach to the design of fuzzy state feedback controllers for continuous-time non-linear systems with input saturation under persistent perturbations. It is assumed that all the states of the Takagi-Sugeno (TS) fuzzy model representing a non-linear system are measurable. Such controllers achieve bounded input bounded output (BIBO) stabilisation in closed loop based on the computation of inescapable ellipsoids. These ellipsoids are computed with linear matrix inequalities (LMIs) that guarantee stabilisation with input saturation and persistent perturbations. In particular, two kinds of inescapable ellipsoids are computed when solving a multiobjective optimization problem: the maximum volume inescapable ellipsoids contained inside the validity domain of the TS fuzzy model and the smallest inescapable ellipsoids which guarantee a minimum *-norm (upper bound of the 1-norm) of the perturbed system. For every initial point contained in the maximum volume ellipsoid, the closed loop will enter the minimum *-norm ellipsoid after a finite time, and it will remain inside afterwards. Consequently, the designed controllers have a large domain of validity and ensure a small value for the 1-norm of closed loop.

Bibo Stabilisation of Continuous–Time Takagi–Sugeno Systems under Persistent Perturbations and Input Saturation

International Journal of Applied Mathematics and Computer Science

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

This paper presents a novel approach to the design of fuzzy state feedback controllers for continuous-time non-linear systems with input saturation under...

Bibo Stabilisation of Continuous–Time Takagi–Sugeno Systems under Persistent Perturbations and Input Saturation

Publié en ligne: 03 oct. 2018

Pages: 457 - 472

Reçu: 23 août 2017

Accepté: 28 mars 2018

DOI: https://doi.org/10.2478/amcs-2018-0035

Mots clés
LMIs, fuzzy systems, non-linear systems, input saturation, disturbances

© 2018 José V. Salcedo, published by Sciendo

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

Bibo Stabilisation of Continuous–Time Takagi–Sugeno Systems under Persistent Perturbations and Input Saturation

Publié en ligne: 03 oct. 2018

Pages: 457 - 472

Reçu: 23 août 2017

Accepté: 28 mars 2018

DOI: https://doi.org/10.2478/amcs-2018-0035

Mots clésLMIs, fuzzy systems, non-linear systems, input saturation, disturbances

© 2018 José V. Salcedo, published by Sciendo

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

Mots clés
LMIs, fuzzy systems, non-linear systems, input saturation, disturbances