${cal H}_{infty}$ State-Feedback Control Design for Fuzzy Systems Using Lyapunov Functions With Quadratic Dependence on Fuzzy Weighting Functions

This paper proposes a method for designing an ${cal H}_{infty}$ state-feedback fuzzy controller for discrete-time Takagi–Sugeno (T-S) fuzzy systems. To derive less conservative ${cal H}_{infty}$ stabilization conditions, this paper enhances the interactions among the fuzzy subsystems using a multiple Lyapunov function with quadratic dependence on fuzzy weighting functions. Besides, for more allocation of the nonlinearity to the fuzzy control system, this paper introduces a slack variable that is quadratically dependent on the one-step-past fuzzy weighting functions as well as the current ones. In the derivation, the ${cal H}_{infty}$ stabilization conditions are formulated in terms of parameterized linear matrix inequalities (PLMIs), which are reconverted into LMI conditions with the help of an efficient relaxation technique.