Global non-quadratic D -stabilization of Takagi–Sugeno systems with piecewise continuous membership functions
| Autor: | Kevin Guelton, Abdelmadjid Cherifi, Valter J. S. Leite, Laurent Arcese |
|---|---|
| Přispěvatelé: | Centre de Recherche en Sciences et Technologies de l'Information et de la Communication - EA 3804 (CRESTIC), Université de Reims Champagne-Ardenne (URCA), Centro Federal de Educação Tecnológica de Minas Gerais (CEFET-MG) |
| Jazyk: | angličtina |
| Rok vydání: | 2019 |
| Předmět: |
Lyapunov function
0209 industrial biotechnology Class (set theory) Applied Mathematics [MATH.MATH-DS]Mathematics [math]/Dynamical Systems [math.DS] Stability (learning theory) 020206 networking & telecommunications 02 engineering and technology Interval (mathematics) [SPI.AUTO]Engineering Sciences [physics]/Automatic [INFO.INFO-AI]Computer Science [cs]/Artificial Intelligence [cs.AI] Computational Mathematics Nonlinear system symbols.namesake 020901 industrial engineering & automation Quadratic equation Takagi sugeno [INFO.INFO-AU]Computer Science [cs]/Automatic Control Engineering 0202 electrical engineering electronic engineering information engineering symbols Piecewise Applied mathematics Mathematics |
| Zdroj: | Applied Mathematics and Computation Applied Mathematics and Computation, Elsevier, 2019, 351, pp.23-36. ⟨10.1016/j.amc.2019.01.031⟩ |
| ISSN: | 0096-3003 |
| DOI: | 10.1016/j.amc.2019.01.031⟩ |
| Popis: | 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. |
| Databáze: | OpenAIRE |
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