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LMI‐based robust sliding control for mismatched uncertain nonlinear systems using fuzzy models
Author(s) -
Liu SungChieh,
Lin ShengFuu
Publication year - 2011
Publication title -
international journal of robust and nonlinear control
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.361
H-Index - 106
eISSN - 1099-1239
pISSN - 1049-8923
DOI - 10.1002/rnc.1789
Subject(s) - control theory (sociology) , fuzzy logic , nonlinear system , fuzzy control system , robust control , stability (learning theory) , exponential stability , mathematics , computer science , control (management) , state (computer science) , mathematical optimization , algorithm , artificial intelligence , physics , quantum mechanics , machine learning
SUMMARY We propose a robust sliding control design method for uncertain Takagi–Sugeno fuzzy models. The uncertain fuzzy systems under consideration have mismatched parameter uncertainties in the state matrix and external disturbances. We make the first attempt to relax the restrictive assumption that each nominal local system model shares the same input channel, which is required in the traditional VSS‐based fuzzy control design methods. We derive the existence conditions of linear sliding surfaces guaranteeing the asymptotic stability in terms of constrained LMIs. We present an LMI characterization of such sliding surfaces. Also, an LMI‐based algorithm is given to design the switching feedback control term so that a stable sliding motion is induced in finite time. Finally, we give two simulation results to show the effectiveness of the proposed method. Copyright © 2011 John Wiley & Sons, Ltd.