Inherent robust stability of driver support systems

Presented are the fact that the transfer function from the front steering a ngle to yaw rate is strictly positive real, irrespective of the uncertain m ass and uncertain velocity, how to determine the positivity margin for this transfer function (some stabilization results are obtained), and how to ch eck the positivity of a controller family. Furthermore, by exploiting the i ntrinsic structure of system equations and uncertainties, a nonconservative PID stabilization criterion for driver support systems is established. Som e interesting results on positivity and connections of PID controllers are shown. Finally, some extreme point results on PID alpha-stabilization are o btained. These results give certain explanations and justifications for the simulation results performed at German Aerospace Research Center.