H∞H∞ state-feedback control for fuzzy systems with input saturation via fuzzy weighting-dependent Lyapunov functions

This paper proposes a method for designing an H∞H∞ state-feedback fuzzy controller for discrete-time Takagi–Sugeno (T–S) fuzzy systems with input saturation. To address the input saturation problem, this paper first formulates a set invariance condition for the T–S fuzzy systems. Then, based on the set invariance condition, this paper establishes H∞H∞ stabilization conditions associated with a fuzzy weighting-dependent Lyapunov function, where the fuzzy controller is designed to be dependent on not only the current-time but also the one-step-past information on the time-varying fuzzy weighting functions. In the derivation, the H∞H∞ stabilization conditions are first formulated in terms of parameterized linear matrix inequalities (PLMIs), and then reconverted into LMIs by an efficient relaxation technique.