A sufficient stability condition for a type of proportional T-S fuzzy control system in the frequency domain

A sufficient stability condition in the frequency domain is presented for a type of muti-rules proportional Takagi-Sugeno (T-S) fuzzy control system by using the technique of loop transformation and the circle criterion. This condition can be utilized to geometrically analyze the global asymptotical stability of such T-S fuzzy control system. Two numerical examples are given to illustrate how to use this condition to analyze the T-S fuzzy control systems.