Real-time estimation of the switching signal for perturbed switched linear systems

We extend previous works of Fliess et al. [2008] on the estimation of the switching signal and of the state for switching linear systems to the perturbed case when the perturbation is structured that is when the perturbation is unknown but known to satisfy a certain differential equation (for example if the perturbation is constant then its time-derivative is zero). We characterize also singular inputs and/or perturbations for which the switched systems become undistinguishable. Several convincing numerical experiments are illustrating our techniques which are easily implementable.