TY - CHAP
T1 - Output feedback control synthesis and stabilization for positive polynomial fuzzy systems under L1 performance
AU - Meng, Aiwen
AU - Lam, Hak Keung
AU - Liu, Fucai
AU - Wang, Ziguang
N1 - Funding Information:
This work is supported in part by the Natural Science Foundation of Hebei Province under Project Number F2019203505; China Scholarship Council and King’s College London.
Publisher Copyright:
© 2020 The authors and IOS Press.
Copyright:
Copyright 2021 Elsevier B.V., All rights reserved.
PY - 2020
Y1 - 2020
N2 - This paper presents the stabilization for positive nonlinear systems using polynomial fuzzy models. To conform better to the practical scenarios that system states are not completely measurable, the static output feedback (SOF) control strategy instead of the state feedback control method is employed to realize the stability and positivity of the positive polynomial fuzzy system (PPFS) with satisfying L1-induced performance. However, some troublesome problems in analysis and control design will follow, such as the non-convex problem. Fortunately, by doing mathematical tricks, the non-convex problem is skillfully dealt with. Furthermore, the neglect of external disturbances may lead to a great negative impact on the performance of positive systems. For the sake of guaranteeing the asymptotic stability and positivity under the satisfaction of the optimal performance of the PPFS, it is significant to take the L1-induced performance requirement into consideration as well. In addition, a linear co-positive Lyapunov function is chosen so that the positivity can be extracted well and the stability analysis becomes simple. By using the sum of squares (SOS) technique, the convex stability and positivity conditions in the form of SOS are derived. Eventually, for illustrating the advantages of the proposed method, a simulation example is shown in the simulation section.
AB - This paper presents the stabilization for positive nonlinear systems using polynomial fuzzy models. To conform better to the practical scenarios that system states are not completely measurable, the static output feedback (SOF) control strategy instead of the state feedback control method is employed to realize the stability and positivity of the positive polynomial fuzzy system (PPFS) with satisfying L1-induced performance. However, some troublesome problems in analysis and control design will follow, such as the non-convex problem. Fortunately, by doing mathematical tricks, the non-convex problem is skillfully dealt with. Furthermore, the neglect of external disturbances may lead to a great negative impact on the performance of positive systems. For the sake of guaranteeing the asymptotic stability and positivity under the satisfaction of the optimal performance of the PPFS, it is significant to take the L1-induced performance requirement into consideration as well. In addition, a linear co-positive Lyapunov function is chosen so that the positivity can be extracted well and the stability analysis becomes simple. By using the sum of squares (SOS) technique, the convex stability and positivity conditions in the form of SOS are derived. Eventually, for illustrating the advantages of the proposed method, a simulation example is shown in the simulation section.
KW - L1 performance
KW - positive polynomial fuzzy system (PPFS)
KW - stability analysis
KW - static output feedback (SOF)
KW - sum of squares (SOS)
UR - http://www.scopus.com/inward/record.url?scp=85101591975&partnerID=8YFLogxK
U2 - 10.3233/FAIA200693
DO - 10.3233/FAIA200693
M3 - Conference paper
AN - SCOPUS:85101591975
T3 - Frontiers in Artificial Intelligence and Applications
SP - 135
EP - 145
BT - Frontiers in Artificial Intelligence and Applications
A2 - Tallon-Ballesteros, Antonio J.
PB - IOS Press BV
T2 - 6th International Conference on Fuzzy Systems and Data Mining, FSDM 2020
Y2 - 13 November 2020 through 16 November 2020
ER -