Stability and stabilization of Takagi-Sugeno fuzzy systems
Mehmet Akar, U. Ozguner · 2003
This paper discusses stability and stabilization of discrete-time and continuous-time Takagi-Sugeno fuzzy systems. Conditions on stability of the open-loop fuzzy system are derived 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 continuous time fuzzy system, different Lyapunov functions generate different results for discrete-time fuzzy systems, quadratic Lyapunov generating the superior of the two. Following a similar approach, stabilization of the open-loop fuzzy system using local parallel distributed compensators is investigated.