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H ∞ sliding mode observer design for a class of nonlinear discrete time‐delay systems: A delay‐fractioning approach
Author(s) -
Hu Jun,
Wang Zidong,
Niu Yugang,
Stergioulas Lampros K.
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.1785
Subject(s) - control theory (sociology) , nonlinear system , weighting , observer (physics) , discrete time and continuous time , exponential stability , mathematics , stability (learning theory) , class (philosophy) , mode (computer interface) , minification , computer science , mathematical optimization , control (management) , medicine , statistics , physics , quantum mechanics , machine learning , operating system , artificial intelligence , radiology
SUMMARY In this paper, the H ∞ sliding mode observer (SMO) design problem is investigated for a class of nonlinear discrete time‐delay systems. The nonlinear descriptions quantify the maximum possible derivations from a linear model, and the system states are allowed to be immeasurable. Attention is focused on the design of a discrete‐time SMO such that the asymptotic stability as well as the H ∞ performance requirement of the error dynamics can be guaranteed in the presence of nonlinearities, time delay and external disturbances. Firstly, a discrete‐time discontinuous switched term is proposed to make sure that the reaching condition holds. Then, by constructing a new Lyapunov–Krasovskii functional based on the idea of ‘delay fractioning’ and by introducing some appropriate free‐weighting matrices, a sufficient condition is established to guarantee the desired performance of the error dynamics in the specified sliding mode surface by solving a minimization problem. Finally, an illustrative example is given to show the effectiveness of the designed SMO design scheme. Copyright © 2011 John Wiley & Sons, Ltd.