This work deals with the design method of robust switched H ∞ PI observer-based control for switched uncertain systems with external disturbances. All sufficient conditions for the robust stability of the closed-loop systems are established by using switched Lyapunov function and LMI/LME framework. Its performances are demonstrated through the vehicle dynamics application to estimate simultaneously lateral speed and road bank angle (unknown input) based on steering vehicle control. Simulations are performed using real data previously recorded by an instrumented vehicle. Keywords: Switched uncertain linear systems, H ∞ norm, LMI/LME, PI observer-based control, lateral speed and road bank angle estimation, steering vehicle control.