TY - GEN
T1 - Relaxed LMI-based stability conditions for fuzzy-model-based control systems under imperfect premise matching
T2 - 2014 11th World Congress on Intelligent Control and Automation, WCICA 2014
AU - Zhao, Yanbin
AU - Xiao, Bo
AU - Liu, Chuang
AU - Li, Hongyi
AU - Lam, H. K.
N1 - Publisher Copyright:
© 2014 IEEE.
PY - 2015/3/2
Y1 - 2015/3/2
N2 - This paper investigates the stability of the fuzzy-model-based control systems under imperfect premise matching that both fuzzy model and fuzzy controller are not required to share the same number of fuzzy rules and the same set of premise membership functions. Under the case of imperfect premise matching, it allows a greater design flexibility for fuzzy controller and is able to lower the implementation complexity when a less number of fuzzy rules and/or some simple membership functions are employed. However, due to the mismatch of the number of fuzzy rules and/or the membership functions, the existing analysis techniques with the parallel distributed compensation (PDC) cannot be applied to deal with the cross term of the membership functions and thus it leads to comparatively conservative stability conditions. In order to relax the stability conditions, we approximate the multiplication of the membership functions and the approximated membership functions exhibit some nice properties in favour of the stability analysis. Through the approximated membership functions, the information of the original membership functions is brought to the stability conditions. As a result, the proposed stability conditions are applied to a specified nonlinear plant characterized by the approximated membership functions rather than a family. A simulation example is given to demonstrate the effectiveness of the proposed approach.
AB - This paper investigates the stability of the fuzzy-model-based control systems under imperfect premise matching that both fuzzy model and fuzzy controller are not required to share the same number of fuzzy rules and the same set of premise membership functions. Under the case of imperfect premise matching, it allows a greater design flexibility for fuzzy controller and is able to lower the implementation complexity when a less number of fuzzy rules and/or some simple membership functions are employed. However, due to the mismatch of the number of fuzzy rules and/or the membership functions, the existing analysis techniques with the parallel distributed compensation (PDC) cannot be applied to deal with the cross term of the membership functions and thus it leads to comparatively conservative stability conditions. In order to relax the stability conditions, we approximate the multiplication of the membership functions and the approximated membership functions exhibit some nice properties in favour of the stability analysis. Through the approximated membership functions, the information of the original membership functions is brought to the stability conditions. As a result, the proposed stability conditions are applied to a specified nonlinear plant characterized by the approximated membership functions rather than a family. A simulation example is given to demonstrate the effectiveness of the proposed approach.
KW - Fuzzy-model-based control
KW - Imperfect premise matching
KW - LMI-based stability analysis
UR - http://www.scopus.com/inward/record.url?scp=84932167828&partnerID=8YFLogxK
U2 - 10.1109/WCICA.2014.7052722
DO - 10.1109/WCICA.2014.7052722
M3 - Conference Proceeding
AN - SCOPUS:84932167828
T3 - Proceedings of the World Congress on Intelligent Control and Automation (WCICA)
SP - 251
EP - 256
BT - Proceeding of the 11th World Congress on Intelligent Control and Automation, WCICA 2014
PB - Institute of Electrical and Electronics Engineers Inc.
Y2 - 29 June 2014 through 4 July 2014
ER -