Reference
Zs. Lendek, R. Babuška, 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.
Downloads
Companion paper
- Zs. Lendek, R. Babuška, and B. De Schutter, "Stability bounds for fuzzy estimation and control - Part II: Output-feedback control," Proceedings of the 2010 IEEE International Conference on Automation, Quality and Testing, Robotics (AQTR 2010), Cluj-Napoca, Romania, May 2010. Paper A-S1-4/3030. (abstract, bibtex, tech. report (pdf))
BibTeX
@inproceedings{LenBab:10-025,
author = {Lendek, {\relax Zs}{\'{o}}fia and Babu{\v{s}}ka, Robert and De
Schutter, Bart},
title = {Stability Bounds for Fuzzy Estimation and Control -- {Part I:
State} Estimation},
booktitle = {Proceedings of the 2010 IEEE International Conference on
Automation, Quality and Testing, Robotics (AQTR 2010)},
address = {Cluj-Napoca, Romania},
month = may,
year = {2010},
note = {Paper A-S1-3/3023}
}