Decentralized techniques for the analysis and control of Takagi-Sugeno fuzzy systems

This paper discusses decentralized parallel distributed compensator design for Takagi-Sugeno (T-S) fuzzy systems. The fuzzy system is viewed as an int erconnection df subsystems some of which are strongly connected, while othe rs being weakly connected. The necessary theory is developed so that one ca n associate this fuzzy system with another one in a higher dimensional spac e, so-called expanded space, design decentralized parallel distributed comp ensators in the expanded space, then contract the solution for implementati on on the original fuzzy system. In this respect, connective stability of t he open loop and closed loop of the interconnected system is analyzed via t he concepts of vector Lyapunov functions and M-matrices. Two different quad ratic and norm-like Lyapunov functions are employed for the subsystems to d erive conditions on stability of the fuzzy system. Unlike the case for the continuous-time fuzzy system, different Lyapunov functions generate differe nt: results for the discrete-time fuzzy system, quadratic Lyapunov generati ng the superior of the two. Following a similar approach, stabilization of the closed-loop fuzzy system using local parallel distributed compensators is investigated. Finally, an example is given to illustrate the issues disc ussed throughout the paper.