TY - JOUR
T1 - More relaxed stability analysis and positivity analysis for positive polynomial fuzzy systems via membership functions dependent method
AU - Han, Meng
AU - Lam, H. K.
AU - Liu, Fucai
AU - Tang, Yinggan
N1 - Funding Information:
The authors are grateful to the financial support of Natural Science Foundation of Hebei Province [grant number F2019203505 ].
Publisher Copyright:
© 2021 Elsevier B.V.
PY - 2022/3/28
Y1 - 2022/3/28
N2 - In this paper, the conservatism source of the positivity and stability analysis results of positive polynomial fuzzy-model-based (PPFMB) control system are studied. Also, in order to improve the flexibility of controller design, a fuzzy controller that does not depend on the membership functions of the fuzzy model is designed. In the existing literatures, it is proved that the LCLF can reduce the conservatism of stability results. However, the LCLF generally results in non-convex conditions which is still a conservatism source. To handle the non-convex conditions, the sector nonlinear concept is applied to handle non-convex terms in stability conditions, and the obstacles caused by mismatched membership functions can be eliminated by PLMF dependent method. In addition, to relax the conservatism caused by the lack of membership functions information, the PLMF dependent positivity analysis are performed for the first time. Meanwhile, PLMF dependent method is extended to stability conditions to obtained more relaxed conditions. Finally, a simulation example is presented to verify the feasibility of this method.
AB - In this paper, the conservatism source of the positivity and stability analysis results of positive polynomial fuzzy-model-based (PPFMB) control system are studied. Also, in order to improve the flexibility of controller design, a fuzzy controller that does not depend on the membership functions of the fuzzy model is designed. In the existing literatures, it is proved that the LCLF can reduce the conservatism of stability results. However, the LCLF generally results in non-convex conditions which is still a conservatism source. To handle the non-convex conditions, the sector nonlinear concept is applied to handle non-convex terms in stability conditions, and the obstacles caused by mismatched membership functions can be eliminated by PLMF dependent method. In addition, to relax the conservatism caused by the lack of membership functions information, the PLMF dependent positivity analysis are performed for the first time. Meanwhile, PLMF dependent method is extended to stability conditions to obtained more relaxed conditions. Finally, a simulation example is presented to verify the feasibility of this method.
KW - Linear copositive Lyapunov function (LCLF)
KW - Piecewise linear membership functions (PLMF) dependent method
KW - Positive polynomial fuzzy-model-based (PPFMB) control systems
KW - Sector nonlinear concept
UR - http://www.scopus.com/inward/record.url?scp=85098772737&partnerID=8YFLogxK
U2 - 10.1016/j.fss.2020.12.015
DO - 10.1016/j.fss.2020.12.015
M3 - Article
AN - SCOPUS:85098772737
SN - 0165-0114
VL - 432
SP - 111
EP - 131
JO - Fuzzy Sets and Systems
JF - Fuzzy Sets and Systems
ER -