Reference
Zs. Lendek, R. Babuška, and B. De Schutter, "Stability of cascaded
Takagi-Sugeno fuzzy systems,"
Proceedings of the 2007 IEEE
International Conference on Fuzzy Systems (FUZZ-IEEE 2007), London, UK,
pp. 505-510, July 2007.
Abstract
A large class of nonlinear systems can be well approximated by Takagi-Sugeno
(TS) fuzzy models, with local models often chosen linear or affine. It is
well-known that the stability of these local models does not ensure the
stability of the overall fuzzy system. Therefore, several stability conditions
have been developed for TS fuzzy systems. We study a special class of nonlinear
dynamic systems, that can be decomposed into cascaded subsystems. These
subsystems are represented as TS fuzzy models. We analyze the stability of the
overall TS system based on the stability of the subsystems. For a general
nonlinear, cascaded system, global asymptotic stability of the individual
subsystems is not sufficient for the stability of the cascade. However, for the
case of TS fuzzy systems, we prove that the stability of the subsystems implies
the stability of the overall system. The main benefit of this approach is that
it relaxes the conditions imposed when the system is globally analyzed,
therefore solving some of the feasibility problems. Another benefit is, that by
using this approach, the dimension of the associated linear matrix inequality
(LMI) problem can be reduced. Applications of such cascaded systems include
multi-agent systems, distributed process control and hierarchical large-scale
systems.
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BibTeX
@inproceedings{LenBab:07-012,
author = {Lendek, {\relax Zs}{\'{o}}fia and Babu{\v{s}}ka, Robert and De
Schutter, Bart},
title = {Stability of Cascaded {Takagi-Sugeno} Fuzzy Systems},
booktitle = {Proceedings of the 2007 IEEE International Conference on Fuzzy
Systems (FUZZ-IEEE 2007)},
address = {London, UK},
pages = {505--510},
month = jul,
year = {2007}
}