Inherent robust stability of driver support systems (Q1962498)

The aim of the paper is to provide some analytical results on PID stabilization of car steering systems, to establish some positive real results for driver support systems, and use these results to solve some stabilization problems. It is shown that the transfer function from the front steering angle to yaw rate is strictly positive real, irrespective of the uncertain mass and uncertain velocity and also it is shown how to determine the positivity margin of the transfer function. Some stabilization results are obtained. By exploiting the intrinsic structure of the system equations and uncertainties, a nonconservative PID stabilization criterion for a driver support system is established. Some extreme point results on PID \(\alpha\)-stabilization are obtained.