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H ∞ observer design for uncertain nonlinear discrete‐time systems with time‐delay: LMI optimization approach
Author(s) -
Sayyaddelshad Saleh,
Gustafsson Thomas
Publication year - 2014
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.3155
Subject(s) - lipschitz continuity , control theory (sociology) , observer (physics) , parametric statistics , discrete time and continuous time , nonlinear system , mathematics , optimization problem , linear matrix inequality , upper and lower bounds , constant (computer programming) , attenuation , mathematical optimization , computer science , control (management) , statistics , physics , mathematical analysis , quantum mechanics , artificial intelligence , optics , programming language
Summary We present a robust H ∞ observer for a class of nonlinear discrete‐time systems. The class under study includes an unknown time‐varying delay limited by upper and lower bounds, as well as time‐varying parametric uncertainties. We design a nonlinear H ∞ observer, by using the upper and lower bounds of the delay, that guarantees asymptotic stability of the estimation error dynamics and is also robust against time‐varying parametric uncertainties. The described problem is converted to a standard optimization problem, which can be solved in terms of linear matrix inequalities (LMIs). Then, we expand the problem to a multi‐objective optimization problem in which the maximum admissible Lipschitz constant and the minimum disturbance attenuation level are the problem objectives. Finally, the proposed observer is illustrated with two examples. Copyright © 2014 John Wiley & Sons, Ltd.