Paper Info
Title
Stability Analysis and Control of Discrete Type-1 and Type-2 TSK Fuzzy Systems: Part I. Stability Analysis
Abstract
This paper introduces sufficient conditions for the exponential stability of type-1 and type-2 Takagi–Sugeno–Kang (TSK) fuzzy systems. A major advantage of the new conditions is that they do not require the existence of a common Lyapunov function and are, therefore, applicable to systems with unstable consequents. In addition, our results include two classes of type-2 TSK systems with type-1 consequents for which no stability tests are available. The use of the conditions in stability testing is demonstrated using simple numerical examples that include cases where methods that are based on a common Lyapunov function fail. The application of the stability test to develop new controller design methodologies is presented in a separate paper (i.e., Part II).
Year
DOI
Venue
2011
10.1109/TFUZZ.2011.2158218
Fuzzy Systems, IEEE Transactions
Keywords
Field
DocType
Lyapunov methods,asymptotic stability,control system analysis,control system synthesis,discrete systems,fuzzy systems,Lyapunov function,Takagi-Sugeno-Kang fuzzy systems,controller design,discrete type-1 TSK fuzzy systems,discrete type-2 TSK fuzzy systems,exponential stability,stability analysis,stability testing,sufficient condition,Stability,Takagi–Sugeno–Kang (TSK) systems,type-2 fuzzy systems
Mathematical optimization,Controller design,Control theory,Common lyapunov function,Stability test,Exponential stability,Fuzzy control system,Numerical stability,Mathematics
Journal
Volume
Issue
ISSN
19
6
1063-6706
Citations 
PageRank 
References 
24
0.88
26
Authors
3
Name
Order
Citations
PageRank
Saeed Jafarzadeh1985.78
Sami M. Fadali213714.82
Assem H. Sonbol3592.29