Relaxed Stability and Performance LMI Conditions for Takagi--Sugeno Fuzzy Systems With Polynomial Constraints on Membership Function Shapes

• Published in: IEEE transactions on fuzzy systems Vol. 16; no. 5; pp. 1328 - 1336
• Main Authors: Sala, A., Arino, C.
• Format: Journal Article
• Language: English
• Published: New York IEEE 01.10.2008; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Control design; Fuzzy control; Fuzzy systems; Linear matrix inequalities; Linear matrix inequality (LMI); Mathematical analysis; Mathematical models; Nonlinearity; Open loop systems; parallel distributed compensation (PDC); polynomial fuzzy systems; Polynomials; quadratic stability; relaxed condition; Shape control; Stability; Sufficient conditions; Systems engineering and theory; Takagi > Sugeno (T > S) fuzzy control; relaxed condition; Takagi-Sugeno fuzzy control; LMI; polynomial fuzzy systems; parallel distributed compensation; quadratic stability
• ISSN: 1063-6706; 1941-0034
• DOI: 10.1109/TFUZZ.2008.926585

Most linear matrix inequality (LMI) fuzzy control results in literature are valid for any membership function, i.e., independent of the actual membership shape. Hence, they are conservative (with respect to other nonlinear control approaches) when specific knowledge of the shapes is available. This paper presents relaxed LMI conditions for fuzzy control that incorporate such shape information in the form of polynomial constraints, generalizing previous works by the authors. Interesting particular cases are overlap (product) bounds and ellipsoidal regions. Numerical examples illustrate the achieved improvements, as well as the possibilities of solving some multiobjective problems. The results also apply to polynomial-in-membership Takagi-Sugeno fuzzy systems.