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 interconnection df subsystems some of which are strongly connected, while others being weakly connected. The necessary theory is developed so that one can associate this fuzzy system with another one in a higher dimensional space, so-called expanded space, design decentralized parallel distributed compensators in the expanded space, then contract the solution for implementation on the original fuzzy system. In this respect, connective stability of the open loop and closed loop of the interconnected system is analyzed via the concepts of vector Lyapunov functions and M-matrices. Two different quadratic and norm-like Lyapunov functions are employed for the subsystems to derive conditions on stability of the fuzzy system. Unlike the case for the continuous-time fuzzy system, different Lyapunov functions generate different: results for the discrete-time fuzzy system, quadratic Lyapunov generating 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 discussed throughout the paper.