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A sliding mode control approach for systems subjected to a norm‐bounded uncertainty
Author(s) -
Sellami Anis,
Arzelier Denis,
M'hiri Radhi,
Zrida Jalel
Publication year - 2006
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.1140
Subject(s) - bounded function , control theory (sociology) , norm (philosophy) , benchmark (surveying) , sliding mode control , linear matrix inequality , mathematical optimization , nonlinear system , convex optimization , mathematics , optimization problem , ideal (ethics) , regular polygon , computer science , control (management) , mathematical analysis , philosophy , physics , geometry , geodesy , epistemology , quantum mechanics , artificial intelligence , political science , law , geography
This paper proposes a design approach of continuous sliding mode control of uncertain systems, the uncertainty being norm bounded. The two steps of the design methodology are investigated. The existence step, in which we choose the sliding surface that gives good behaviour during the sliding mode, is formulated as a pole assignment of linear uncertain system in a sector through convex optimization. The solution to this problem is therefore numerically tractable via linear matrix inequalities (LMI) optimization. In the reaching step, we propose a continuous nonlinear control strategy ensuring a bounded motion about the ideal sliding mode, thus approximating the ideal dynamic behaviour in the presence of uncertainty. Finally, the validity and the applicability of this approach are illustrated by a flight stabilization benchmark example. Copyright © 2006 John Wiley & Sons, Ltd.