Reference:
Zs. Lendek,
R. Babuska, and
B. De Schutter,
"Stability bounds for fuzzy estimation and control - Part I: State
estimation," Proceedings of the 2010 IEEE International Conference
on Automation, Quality and Testing, Robotics (AQTR 2010),
Cluj-Napoca, Romania, May 2010. Paper A-S1-3/3023.
Abstract:
Analysis and observer design for nonlinear systems have long been
investigated, but no generally applicable methods exist as yet. 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. 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 is designed based on an approximate fuzzy
model and applied to the original nonlinear system. It is shown that
in general, exponential stability of the estimation error dynamics
cannot be obtained. However, the estimation error is bounded. This
bound is computed based on the approximation error and the Lyapunov
function used. The results are illustrated using simulation examples.