Reference:
Zs. Lendek,
R. Babuska, and
B. De Schutter,
"Stability analysis and observer design for decentralized TS fuzzy
systems," Proceedings of the 2008 IEEE International Conference on
Fuzzy Systems (FUZZ-IEEE 2008), Hong Kong, pp. 631-636, June
2008.
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. Stability conditions
developed for TS fuzzy systems in general rely on the feasibility of
an associated system of linear matrix inequalities, whose complexity
may grow exponentially with the number of rules. We study distributed
systems, where the subsystems are represented as TS fuzzy models. For
such systems, a centralized analysis is often unfeasible. We analyze
the stability of the overall TS system based on the stability of the
subsystems and the strength of the interconnection terms. For
naturally distributed applications, such as multi-agent systems, when
adding new subsystems "on-line", the construction and tuning of a
centralized observer is often intractable. Therefore, we also propose
a decentralized approach to observer design. Applications of such
systems include distributed process control, traffic networks, and
economic systems.