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The estimation of friction coefficient for a vehicle when it traverses on different surfaces has been an important issue. In this work, the longitudinal vehicle dynamics, the torsional tyre dynamics and the non-linear LuGre friction dynamics are integrated to model the quarter vehicle dynamics. The road adhesion coefficient in the vehicle dynamics is unknown and varies with the contact surface. To address this issue, the authors consider a class of non-linear uncertain systems that covers thedoi:10.1049/iet-cta.2013.0593 fatcat:mefak63fp5h4ngmy5vpesvfjfa