Paper Info
Title
Membership-function-dependent stability analysis and local controller design for T–S fuzzy systems: A space-enveloping approach
Abstract
For Takagi–Sugeno (T–S) fuzzy systems, relaxed stability conditions are obtained by more effectively enveloping the trajectory of the membership functions (MFs) in a unified space of MF. Considering an open-loop T–S fuzzy system, the system premise variables operation domain can be divided into a series of subdomains. Based on an MF unified space extremum calculation technique, the MFs extremum values in each premise variable corresponding to the unified space subdomain are calculated. With these extremes, a tight local convex polyhedron enveloping the MF trajectory is constructed in each subdomain. Thus, linear matrix inequality (LMI) stability conditions are derived via a piecewise Lyapunov function. Then, a state-feedback local controller is designed to close the system loop. From a geometric viewpoint, MF extremum enveloping and piecewise linear-approximation methods are both utilized to achieve relaxed stability and robustness conditions. Finally, several examples are adopted to illustrate the metrics of the proposed approaches.
Year
DOI
Venue
2021
10.1016/j.ins.2020.09.043
Information Sciences
Keywords
DocType
Volume
Takagi–Sugeno fuzzy system,Membership function,Piecewise Lyapunov function,Local controller,Conservatism
Journal
548
ISSN
Citations 
PageRank 
0020-0255
2
0.36
References 
Authors
0
4
Name
Order
Citations
PageRank
Hua Zheng141.13
Wenbo Xie262.90
H. K. Lam33618193.15
Likui Wang415311.05