New LMI Condition for Observer-Based $\mathcal{H}_{\infty}$ Stabilization of a Class of Nonlinear Discrete-Time Systems

In this paper a new LMI (linear matrix inequality) condition is provided for the observer-based $\mathcal{H}_{\infty}$ stabilization of a class of nonlinear discrete-time systems. With the proposed design methodology, the observer and controller gains are computed simultaneously by solving only one...

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Bibliographic Details
Published in:SIAM journal on control and optimization 2013-01, Vol.51 (1), p.784-800
Main Authors: Grandvallet, B, Zemouche, A, Souley-Ali, H, Boutayeb, M
Format: Article
Language:English
Subjects:
Inequality
Links
Mathematical analysis
Mathematical models
Methods
Nonlinearity
Observers
Robots
Stabilization
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Summary:In this paper a new LMI (linear matrix inequality) condition is provided for the observer-based $\mathcal{H}_{\infty}$ stabilization of a class of nonlinear discrete-time systems. With the proposed design methodology, the observer and controller gains are computed simultaneously by solving only one inequality. Based on the Lyapunov theory and the use of mathematical artifacts such as matrix decomposition and the Young relation, the novel sufficient synthesis condition is expressed in terms of LMI, which can be easily solved by numerical tools. An application to a flexible link robot manipulator is provided to show the consistency of the proposed approach. A second numerical example is devoted to demonstrating the superiority and the lower conservatism of the proposed LMI compared to those available in the literature. [PUBLICATION ABSTRACT]
ISSN:0363-0129
1095-7138
DOI:10.1137/11085623X