Robust LQ control of ABS based on polytopic representation using descriptor representation and linear fractional transformation

In this paper, a method is proposed to guarantee the robust stability for anti-lock braking system (ABS). The objective of ABS is to maintain the slip rate at the optimal value in any road condition. The dynamics of ABS depends rationally on the uncertain parameters, which are car velocity and the coefficient of friction between tire and road. The robust stability is required to design ABS with respect to these uncertain parameters. Descriptor representation and linear fractional transformation (LFT) are adopted to obtain an equivalent polytopic representation of dynamics, which is multi-affine to the uncertain parameters. The problem can be formulated as solving a finite set of linear matrix inequalities (LMIs) by using polytopic representation. The effectiveness of the proposed method is verified by simulations and experiments.