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

Abstract

This paper proposes a method for designing an 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 ∞ 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 ∞ stabilization conditions are first formulated in terms of parameterized linear matrix inequalities (PLMIs), and then reconverted into LMIs by an efficient relaxation technique.