A new parameter-dependent Lyapunov function approach for robust control

In this paper, we extends the existing results on the H∞ control for continuous-time T-S (Takagi-Sugeno) fuzzy systems. A new fuzzy Lyapunov function is considered for ensuring system stability and guaranteed H∞ performance with parallel distributed compensation (PDC). In addition, two slack variables are introduced to provide extra free dimensions in the solution space for the H∞ control problem. This together with the freedom provided by the fuzzy Lyapunov function directly leads to performance improvement and reduction of conservativeness. A numerical example of the control of an inverted pendulum and cart system is given to demonstrate the effectiveness of the proposed method. Comparisons with some of the existing methods are provided.