Reference
Zs. Lendek, R. Babuška, and B. De Schutter, "Stability of cascaded fuzzy
systems and observers,"
IEEE Transactions on Fuzzy
Systems, vol. 17, no. 3, pp. 641-653, June 2009.
Abstract
A large class of nonlinear systems can be well approximated by Takagi-Sugeno
(TS) fuzzy models, with linear or affine consequents. It is well-known that the
stability of these consequent 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, represented as TS
fuzzy models. We analyze the stability of the overall TS system based on the
stability of the subsystems, and 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,
thereby 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. For naturally distributed applications, such as
multi-agent systems, the construction and tuning of a centralized observer may
not be feasible. Therefore, we extend the cascaded approach also to observer
design, and use fuzzy observers to individually estimate the states of these
subsystems. A theoretical proof of stability and simulation examples are
presented. The results show that the distributed observer achieves the same
performance as the centralized one, while leading to increased modularity,
reduced complexity, lower computational costs, and easier tuning. Applications
of such cascaded systems include multi-agent systems, distributed process
control, and hierarchical large-scale systems.
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BibTeX
@article{LenBab:08-001,
author = {Lendek, {\relax Zs}{\'{o}}fia and Babu{\v{s}}ka, Robert and De
Schutter, Bart},
title = {Stability of Cascaded Fuzzy Systems and Observers},
journal = {IEEE Transactions on Fuzzy Systems},
volume = {17},
number = {3},
pages = {641--653},
month = jun,
year = {2009}
}