Reference:
Zs. Lendek,
R. Babuska, 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.