Global non-quadratic D-stabilization of Takagi–Sugeno systems with piecewise continuous membership functions

• Published in: Applied mathematics and computation Vol. 351; pp. 23 - 36
• Main Authors: Cherifi, Abdelmadjid, Guelton, Kevin, Arcese, Laurent, Leite, Valter J.S.
• Format: Journal Article
• Language: English
• Published: Elsevier Inc 15-06-2019; Elsevier
• Subjects: [formula omitted]-stability; Artificial Intelligence; Automatic; Automatic Control Engineering; Computer Science; Dynamical Systems; Engineering Sciences; Global non-quadratic design; Linear matrix inequalities; Mathematics; Non-PDC controllers; Takagi–Sugeno models; D-stability; Global non-quadratic design; Non-PDC controllers; Linear matrix inequalities; Takagi–Sugeno models
• ISSN: 0096-3003; 1873-5649
• DOI: 10.1016/j.amc.2019.01.031

This paper deals with the non-quadratic stabilization of Takagi–Sugeno (T-S) models with D-stability constraints. Based on a recently proposed Non-Quadratic Lyapunov Function (NQLF), which involves the mean values of the membership functions (MFs) over a given time interval, three theorems are proposed for the design of non-Parallel Distributed Compensation (non-PDC) controllers satisfying closed-loop D-stability specifications. Despite previous non-quadratic approaches and thanks to the nature of the considered NQLF, it is highlighted that the proposed LMI-based procedures not only apply for the global non-quadratic D-stabilization of T-S models, but also for a larger class of T-S models with piecewise membership functions (i.e. a class of switching nonlinear systems), since no requirement is needed regarding to the bounds of the MFs derivatives. The effectiveness of the proposed LMI-based conditions and their relative degrees of conservatism, compared with previous quadratic D-stabilization results, are illustrated through an academic example involving piecewise membership functions.