  Automated Vehicle Path Following Control (PFC) is an advanced control system
that can regulate the vehicle into a collision-free region in the presence of
other objects on the road. Common collision avoidance functions, such as
forward collision warning and automatic emergency braking, have recently been
developed and equipped on production vehicles. However, it is impossible to
develop a perfectly precise vehicle model when the vehicle is driving. Most
PFCs did not consider uncertainties in the vehicle model, external
disturbances, and parameter variations at the same time. To address the issues
associated with this important feature and function in autonomous driving, a
new vehicle PFC is proposed using a robust model predictive control (MPC)
design technique based on matrix inequality and the theoretical approach of the
hybrid $\&$ switched system. The proposed methodology requires a combination of
continuous and discrete states, e.g. regulating the continuous states of the AV
(e.g., velocity and yaw angle) and discrete switching of the control strategy
that affects the dynamic behaviors of the AV under different driving speeds.
Firstly, considering bounded model uncertainties, and norm-bounded external
disturbances, the system states and control matrices are modified.
