Stability analysis and observer design for decentralized TS fuzzy systems

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.