Piecewise-Takagi-Sugeno asymptotically exact estimation of the domain of attraction of nonlinear systems

Abstract

[EN] This report generalises recent results on stability analysis and estimation of the domain of attraction of nonlinear systems via exact piecewise affine Takagi Sugeno models. Algorithms in the form of linear matrix inequalities are proposed that produce progressively better estimates which are proved to asymptotically render the actual domain of attraction; regions already proven to belong to such domain of attraction can be removed and the estimate can contain significant portions of the modelling region boundary; in this way, level-set approaches in prior literature can be significantly improved. Illustrative examples and comparisons are provided. (C) 2016 The Franklin Institute. Published by Elsevier Ltd. All rights reserved.The authors gratefully acknowledge the support of the following institutions: Project Ciencia Basica SEP-CONACYT CB-168406, the CONACyT/COECYT Sonora scholarship 383252, project DPI2016-81002-R (Spanish government, MINECO), and the scholarship GRISOLIA/2014/006 from Generalitat Valenciana (regional government).Gonzalez-German, IT.; Sala, A.; Bernal Reza, MÁ.; Robles-Ruiz, R. (2017). Piecewise-Takagi-Sugeno asymptotically exact estimation of the domain of attraction of nonlinear systems. Journal of the Franklin Institute. 354(3):1514-1541. https://doi.org/10.1016/j.jfranklin.2016.11.033S15141541354