Graphical L2-stability analysis of Takagi-Sugeno control systems in the frequency domain

In this paper, the upper bound of the L2-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 L2-gain, the L2-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 L2-stability of certain kind of T-S fuzzy control system in the frequency domain. One numerical example is presented to illustrate how the L2-stability of the simplified continuous-time T-S fuzzy system can be graphically examined.