TY - JOUR
T1 - Static Output Feedback Stabilization of Positive Polynomial Fuzzy Systems
AU - Meng, Aiwen
AU - Lam, Hak Keung
AU - Yu, Yan
AU - Li, Xiaomiao
AU - Liu, Fucai
PY - 2017/8/5
Y1 - 2017/8/5
N2 - This paper deals with the static output feedback control problem for positive polynomial fuzzy-model-based (PPFMB) control systems that the positive polynomial fuzzy model does not need to share the same premise membership functions with the static output feedback polynomial fuzzy controller. Unlike the state feedback control case, the static output feedback control usually leads to non-convex stability conditions. To circumvent the problem, an approach is employed to transform the nonconvex stability conditions into convex ones by introducing a nonsingular transformation matrix. Initially, the conditions guaranteeing the resultant closed-loop systems to be positive and asymptotically stable are obtained. Moreover, the divisional approximated membership functions which carry the local information of the membership functions are employed to facilitate the stability analysis and controller synthesis. The relaxed stability conditions in terms of sum of squares (SOS) are obtained based on Lyapunov stability theory. Finally, a simulation example is given to testify the validity of the analysis result.
AB - This paper deals with the static output feedback control problem for positive polynomial fuzzy-model-based (PPFMB) control systems that the positive polynomial fuzzy model does not need to share the same premise membership functions with the static output feedback polynomial fuzzy controller. Unlike the state feedback control case, the static output feedback control usually leads to non-convex stability conditions. To circumvent the problem, an approach is employed to transform the nonconvex stability conditions into convex ones by introducing a nonsingular transformation matrix. Initially, the conditions guaranteeing the resultant closed-loop systems to be positive and asymptotically stable are obtained. Moreover, the divisional approximated membership functions which carry the local information of the membership functions are employed to facilitate the stability analysis and controller synthesis. The relaxed stability conditions in terms of sum of squares (SOS) are obtained based on Lyapunov stability theory. Finally, a simulation example is given to testify the validity of the analysis result.
KW - Positive Polynomial Fuzzy-Model-Based (PPFMB) Control Systems
KW - Stability Analysis
KW - Static Output Feedback Control
KW - Sum of Squares (SOS)
UR - http://www.scopus.com/inward/record.url?scp=85028955088&partnerID=8YFLogxK
U2 - 10.1109/TFUZZ.2017.2736964
DO - 10.1109/TFUZZ.2017.2736964
M3 - Article
AN - SCOPUS:85028955088
SN - 1063-6706
JO - IEEE Transactions on Fuzzy Systems
JF - IEEE Transactions on Fuzzy Systems
ER -