Graphical analysis of Takagi–Sugeno control systems in the frequency domain

In this paper, the upper bound of the L 2 -gain of the continuous-time SISO Takagi–Sugeno (T–S) fuzzy system is first graphically obtained in the frequency domain. Based on this upper bound of the L 2 -gain , the L 2 -stability of the above T–S fuzzy control system is next investigated by using the small gain theorem and circle criterion. Two sufficient conditions are derived, which can be employed to graphically investigate the L 2 -stability of certain kind of T–S fuzzy control system in the frequency domain. One numerical example is presented to illustrate how the L 2 -stability of the simplified continuous-time T–S fuzzy system can be graphically examined.