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A new approach for the design of robust H∞ sliding mode observer for Steer-by-Wire (SBW) systems with parametric uncertainties and sensor faults is proposed based on linear matrix inequalities (LMIs). The resulting H∞ observer guarantees asymptotic stability of the estimation error dynamics and is robust against parametric uncertainties. A sensor fault estimation scheme is presented where the estimated signal can approximate the fault signal to any accuracy. The effectiveness of the proposed approach is verified by simulations.