Journal
INTERNATIONAL JOURNAL OF ROBUST AND NONLINEAR CONTROL
Volume 22, Issue 16, Pages 1806-1826Publisher
WILEY-BLACKWELL
DOI: 10.1002/rnc.1785
Keywords
sliding mode observer; discrete-time systems; nonlinear systems; time delay; H?8? performance
Funding
- National Natural Science Foundation of China [61074041, 61028008, 10771047]
- Engineering and Physical Sciences Research Council (EPSRC) of the UK [GR/S27658/01]
- Royal Society of the UK
- Alexander von Humboldt Foundation of Germany
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In this paper, the H?8? 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?8? 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 LyapunovKrasovskii 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 (c) 2011 John Wiley & Sons, Ltd.
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