Paper Info
Title
Stability Analysis and Control of Discrete Type-1 and Type-2 TSK Fuzzy Systems: Part II. Control Design
Abstract
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.
Year
DOI
Venue
2011
10.1109/TFUZZ.2011.2158219
Fuzzy Systems, IEEE Transactions
Keywords
Field
DocType
Lyapunov methods,PI control,control system synthesis,fuzzy systems,linear matrix inequalities,stability,state feedback,LMI,Lyapunov function,Takagi-Sugeno-Kang fuzzy systems,control system design,discrete type-1 fuzzy systems,linear matrix inequalities,proportional-integral controllers,stability analysis,state feedback,type-2 TSK fuzzy systems,Feedback control,Takagi–Sugeno–Kang (TSK) systems,type-2 fuzzy systems
Convergence (routing),Mathematical optimization,Control theory,Physical system,Matrix (mathematics),Control theory,Fuzzy logic,Stability conditions,Exponential stability,Fuzzy control system,Mathematics
Journal
Volume
Issue
ISSN
19
6
1063-6706
Citations 
PageRank 
References 
19
0.72
30
Authors
3
Name
Order
Citations
PageRank
Saeed Jafarzadeh1985.78
Sami M. Fadali213714.82
Assem H. Sonbol3592.29