An LMI approach to slip ratio control of vehicle Antilock braking systems

In this paper, the state equation for the dynamics of quarter car is established, and the nonlinear Antilock braking system is transformed into linear uncertain system model. So the stability problem of nonlinear Antilock braking systems becomes the robust stability problem of linear uncertain systems. Sliding mode control approach is employed to guarantee robust stability of linear uncertain systems. The stable sliding surface is designed by using linear matrix inequalities (LMI) to reduce the influence of mismatched uncertainties. Moreover the design of sliding mode control law is presented also. The system robust stability can be guaranteed and the chattering around the sliding surface in sliding mode control is obviously reduced by the proposed approach.