— In this work, a Continuous-Time Switched H ∞ Proportional-Integral (CTSH ∞ PI) observer is presented. The estimation method is based on a proportional-integral observer introduced by [13], [11], [12]. The estimation method is used to estimate simultaneously the state variables and unknown inputs of switched systems. A design method is established using a common Lyapunov function and H ∞ norm. Its stability and global convergence conditions are proved and expressed in term of LMIs. All conditions are established under given switching signals. The estimation method is applied in vehicle dynamics to estimate simultaneously the vehicle sideslip angle and road bank angle. Moreover, the switching signal is deduced from measured premise variables. Simulation tests with experimental data are included to demonstrate the advantage of this method.