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Design of robust nonfragile H ∞ controller for uncertain nonlinear polynomial systems
Author(s) -
Rezgui Marwa,
Ayadi Hela Belkhiria,
Benhadj Braiek Naceur
Publication year - 2018
Publication title -
optimal control applications and methods
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.458
H-Index - 44
eISSN - 1099-1514
pISSN - 0143-2087
DOI - 10.1002/oca.2466
Subject(s) - control theory (sociology) , kronecker product , mathematics , nonlinear system , robust control , linear matrix inequality , polynomial , controller (irrigation) , bounded function , lyapunov function , linear system , kharitonov's theorem , kronecker delta , mathematical optimization , control (management) , computer science , matrix polynomial , mathematical analysis , physics , quantum mechanics , artificial intelligence , agronomy , biology , square free polynomial
Summary This paper is concerned with the robust H ∞ nonfragile controller design for a particular class of nonlinear systems, namely, the perturbed polynomial systems, which are subject to unstructured bounded uncertainties in both the system model and the control law. Combining the Lyapunov stability theory, properties of linear matrix inequality, and Kronecker product properties, a sufficient condition of robust H ∞ nonfragile control design is proposed. More specifically, we propose a robust H ∞ controller of nonlinear polynomial systems with additive unstructured uncertainties and variation in the control law itself that guarantee the stability and the attenuation of external perturbations. Two examples are provided to illustrate the effectiveness of the proposed approach.