Reference:
Zs. Lendek,
R. Babuska, and
B. De Schutter,
"Stability bounds for fuzzy estimation and control," Control
Engineering and Applied Informatics, vol. 12, no. 3, pp. 3-12,
2010.
Abstract:
A large class of nonlinear systems can be well approximated by
Takagi-Sugeno fuzzy models, for which methods and algorithms have been
developed to analyze their stability and to design observers and
controllers. However, results obtained for Takagi-Sugeno fuzzy models
are in general not directly applicable to the original nonlinear
system. In this paper, we investigate what conclusions can be drawn
and what guarantees can be expected when an observer or a state
feedback controller is designed based on an approximate fuzzy model
and applied to the original nonlinear system. We also investigate the
case when an observer-based controller is designed for an approximate
model and then applied to the original nonlinear system. In
particular, we consider that the scheduling vector used in the
membership functions of the observer depends on the states that have
to be estimated. The results are illustrated using simulation
examples.