Observer-Based Fuzzy Controller Design for Nonlinear Discrete-Time Singular Systems via Proportional Derivative Feedback Scheme

This paper investigates the observer-based fuzzy controller design method for nonlinear discrete-time singular systems that are represented by Takagi-Sugeno (T-S) fuzzy models. At first, the nonlinearity can be well-approximated with several local linear input-output relationships. The parallel dist...

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Bibliographic Details
Published in:Applied sciences 2021-03, Vol.11 (6), p.2833
Main Authors: Chang, Wen-Jer, Tsai, Ming-Hsuan, Pen, Chin-Lin
Format: Article
Language:English
Subjects:
Control methods
Control systems design
Controllers
Design
Discrete time systems
Feedback
Fuzzy sets
Linear matrix inequalities
nonlinear singular systems
Nonlinearity
observer design
Optimization
Proportional derivative
proportional derivative control
Stability criteria
T-S fuzzy model
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Summary:This paper investigates the observer-based fuzzy controller design method for nonlinear discrete-time singular systems that are represented by Takagi-Sugeno (T-S) fuzzy models. At first, the nonlinearity can be well-approximated with several local linear input-output relationships. The parallel distributed compensation (PDC) technology and the proportional derivative (PD) feedback scheme are then employed to construct the observer-based fuzzy controller. To solve the problem of unmeasured states, the impulsive phenomenon of singular systems, and the PD scheme’s reasonableness, a novel observer-based fuzzy controller is developed. By using the Lyapunov theory and projection lemma, the stability criteria are built in terms of linear matrix inequalities (LMI). Moreover, the gains of fuzzy controller and fuzzy observer can be calculated synchronously by using convex optimization algorithms. Finally, a biological economic system is provided to verify the effectiveness of the proposed fuzzy control method.
ISSN:2076-3417
2076-3417
DOI:10.3390/app11062833