Controller Design for Discrete-Time Descriptor Models: A Systematic LMI Approach

This paper provides a systematic way to generalize the controller design for discrete-time nonlinear descriptor models. The controller synthesis is done using a Takagi-Sugeno representation of the descriptor models and linear matrix inequalities. We propose approaches to exploit the discrete-time na...

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Bibliographic Details
Published in:IEEE transactions on fuzzy systems 2015-10, Vol.23 (5), p.1608-1621
Main Authors: Estrada-Manzo, Victor, Lendek, Zsofia, Guerra, Thierry Marie, Pudlo, Philippe
Format: Article
Language:English
Subjects:
Automatic
Computational modeling
Controller design
Controllers
Delays
Design engineering
Dynamics
Engineering Sciences
Gain
Indexes
Linear matrix inequalities
linear matrix inequality
Lyapunov functions
Lyapunov methods
Mathematical models
Mechanical systems
non-quadratic Lyapunov function
nonlinear descriptor model
Representations
Synthesis
Systematics
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Summary:This paper provides a systematic way to generalize the controller design for discrete-time nonlinear descriptor models. The controller synthesis is done using a Takagi-Sugeno representation of the descriptor models and linear matrix inequalities. We propose approaches to exploit the discrete-time nature of the problem by using delayed Lyapunov functions, which allow delayed controller gains. In addition, the well-known Finsler's Lemma is used to avoid the explicit substitution of the closed-loop dynamics. Examples are provided to show the effectiveness of the proposed results.
ISSN:1063-6706
1941-0034
DOI:10.1109/TFUZZ.2014.2371029