Stability Analysis and Control of Discrete Type-1 and Type-2 TSK Fuzzy Systems: Part II. Control Design

This paper proposes a new control system design methodology for type-1 and type-2 Takagi-Sugeno-Kang (TSK) fuzzy systems that are based on new stability conditions. The stability conditions are discussed in a companion paper (Part I) and are used in the proofs of our main results. A major advantage...

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Bibliographic Details
Published in:IEEE transactions on fuzzy systems 2011-12, Vol.19 (6), p.1001-1013
Main Authors: Jafarzadeh, S., Fadali, M. S., Sonbol, A. H.
Format: Article
Language:English
Subjects:
Control design
Control systems
Controllers
Convergence
Design
Design engineering
Design methodology
Feedback control
Fuzzy systems
Lyapunov functions
Mathematical models
Methodology
Stability
Stability analysis
Studies
Takagi-Sugeno-Kang (TSK) systems
Takagi-Sugeno-Kang model
type-2 fuzzy systems
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Summary:This paper proposes a new control system design methodology for type-1 and type-2 Takagi-Sugeno-Kang (TSK) fuzzy systems that are based on new stability conditions. The stability conditions are discussed in a companion paper (Part I) and are used in the proofs of our main results. A major advantage of the new methodology is that it does not require a common Lyapunov function and is therefore applicable to systems with nonstabilizable consequents. Our controllers include fuzzy type-1 proportional and proportional-integral (PI) controllers, as well as constant state feedback for the same systems. The controller results in an exponentially stable system, and the designer can specify the rate of exponential convergence. The controller designs can be tested by the usage of linear matrix inequalities (LMIs). The design methodology is demonstrated by the usage of simple examples where methods that are based on a common Lyapunov function fail and physical systems where the new methodology provides better performance.
ISSN:1063-6706
1941-0034
DOI:10.1109/TFUZZ.2011.2158219