Simultaneous estimation of the state and the unknown inputs for a class of switched linear systems

In this paper, an observer for Switched Linear Systems (SLS) with unknown inputs is designed. LMI conditions, guaranteeing the asymptotic convergence of the observer derived through multiple Lyapunov functions and LMI region. This is done by decoupling a subset of the system states from the unknown inputs and by estimating the states thanks to a like Luenberger observer. Then, an estimator for the reconstruction of the unknown inputs from the estimated state and the derivative of the system outputs using a robust exact differentiator is proposed.