TY - JOUR
T1 - Relaxed stabilization criterion for T-S fuzzy systems by minimum-type piecewise-lyapunov-function-based switching fuzzy controller
AU - Chen, Ying Jen
AU - Ohtake, Hiroshi
AU - Tanaka, Kazuo
AU - Wang, Wen June
AU - Wang, Hua O.
N1 - Funding Information:
Manuscript received February 14, 2011; revised August 5, 2011 and December 16, 2011; accepted March 1, 2012. Date of publication April 25, 2012; date of current version November 27, 2012. This work was supported by the National Science Council of Taiwan under Grant NSC-98-2221-E-008-119-MY3.
PY - 2012
Y1 - 2012
N2 - This paper proposes the minimum-type piecewise-Lyapunov-function-based switching fuzzy controller that switches accompanying the piecewise Lyapunov function. By applying this switching fuzzy controller with the minimum-type piecewise Lyapunov function, the relaxed stabilization criterion is obtained for continuous Takagi-Sugeno (T-S) fuzzy systems. Some conditions of the relaxed stabilization criterion are represented by bilinear matrix inequalities (BMIs), which contain some bilinear terms as the product of a full matrix and a scalar. According to the literature, the path-following method is very effective for this kind of BMI problem; hence, it is utilized to obtain solutions of the criterion. Xie etal. in 1997 chose two types (i.e., minimum type and maximum type) of piecewise Lyapunov functions as the Lyapunov function candidates. The reasons for why this study only chooses the minimum-type piecewise Lyapunov function as the Lyapunov function candidate are illustrated. Moreover, the numerical example shows the relaxation of the proposed criterion.
AB - This paper proposes the minimum-type piecewise-Lyapunov-function-based switching fuzzy controller that switches accompanying the piecewise Lyapunov function. By applying this switching fuzzy controller with the minimum-type piecewise Lyapunov function, the relaxed stabilization criterion is obtained for continuous Takagi-Sugeno (T-S) fuzzy systems. Some conditions of the relaxed stabilization criterion are represented by bilinear matrix inequalities (BMIs), which contain some bilinear terms as the product of a full matrix and a scalar. According to the literature, the path-following method is very effective for this kind of BMI problem; hence, it is utilized to obtain solutions of the criterion. Xie etal. in 1997 chose two types (i.e., minimum type and maximum type) of piecewise Lyapunov functions as the Lyapunov function candidates. The reasons for why this study only chooses the minimum-type piecewise Lyapunov function as the Lyapunov function candidate are illustrated. Moreover, the numerical example shows the relaxation of the proposed criterion.
KW - Bilinear matrix inequality (BMI)
KW - path-following method
KW - piecewise Lyapunov function
KW - relaxed stabilization criterion
KW - switching fuzzy controller
KW - Takagi-Sugeno (T-S) fuzzy system
UR - http://www.scopus.com/inward/record.url?scp=84870508767&partnerID=8YFLogxK
U2 - 10.1109/TFUZZ.2012.2196049
DO - 10.1109/TFUZZ.2012.2196049
M3 - 期刊論文
AN - SCOPUS:84870508767
SN - 1063-6706
VL - 20
SP - 1166
EP - 1173
JO - IEEE Transactions on Fuzzy Systems
JF - IEEE Transactions on Fuzzy Systems
IS - 6
M1 - 6189778
ER -