TY - JOUR
T1 - Stability analysis of interval type-2 fuzzy-model-based control systems
AU - Lam, H. K.
AU - Seneviratne, Lakmal D.
N1 - Funding Information:
Manuscript received June 25, 2007; revised October 1, 2007. This work was supported by the Division of Engineering, King’s College London, London, U.K. This paper was recommended by Associate Editor H.-X. Li. The authors are with the Division of Engineering, King’s College London, WC2R 2LS London, U.K. Digital Object Identifier 10.1109/TSMCB.2008.915530
PY - 2008/6
Y1 - 2008/6
N2 - This paper presents the stability analysis of interval type-2 fuzzy-model-based (FMB) control systems. To investigate the system stability, an interval type-2 Takagi-Sugeno (T-S) fuzzy model, which can be regarded as a collection of a number of type-1 T-S fuzzy models, is proposed to represent the nonlinear plant subject to parameter uncertainties. With the lower and upper membership functions, the parameter uncertainties can be effectively captured. Based on the interval type-2 T-S fuzzy model, an interval type-2 fuzzy controller is proposed to close the feedback loop. To facilitate the stability analysis, the information of the footprint of uncertainty is used to develop some membership function conditions, which allow the introduction of slack matrices to handle the parameter uncertainties in the stability analysis. Stability conditions in terms of linear matrix inequalities are derived using a Lyapunov-based approach. Simulation examples are given to illustrate the effectiveness of the proposed interval type-2 FMB control approach.
AB - This paper presents the stability analysis of interval type-2 fuzzy-model-based (FMB) control systems. To investigate the system stability, an interval type-2 Takagi-Sugeno (T-S) fuzzy model, which can be regarded as a collection of a number of type-1 T-S fuzzy models, is proposed to represent the nonlinear plant subject to parameter uncertainties. With the lower and upper membership functions, the parameter uncertainties can be effectively captured. Based on the interval type-2 T-S fuzzy model, an interval type-2 fuzzy controller is proposed to close the feedback loop. To facilitate the stability analysis, the information of the footprint of uncertainty is used to develop some membership function conditions, which allow the introduction of slack matrices to handle the parameter uncertainties in the stability analysis. Stability conditions in terms of linear matrix inequalities are derived using a Lyapunov-based approach. Simulation examples are given to illustrate the effectiveness of the proposed interval type-2 FMB control approach.
KW - Fuzzy control
KW - Interval type-2 fuzzy model
KW - Stability analysis
UR - http://www.scopus.com/inward/record.url?scp=44849116631&partnerID=8YFLogxK
U2 - 10.1109/TSMCB.2008.915530
DO - 10.1109/TSMCB.2008.915530
M3 - Article
C2 - 18558528
AN - SCOPUS:44849116631
SN - 1083-4419
VL - 38
SP - 617
EP - 628
JO - IEEE Transactions on Systems, Man, and Cybernetics, Part B: Cybernetics
JF - IEEE Transactions on Systems, Man, and Cybernetics, Part B: Cybernetics
IS - 3
ER -