G. Ferrari-Trecate and M. Gati. Observability analysis and state observers for automotive powertrains with backlash: a hybrid system approach. International Journal of Control , 79(5):496--507, 2006.
In this paper, the observability properties of automotive powertrains with backlash areanalysed. We model the powertrain as a hybrid system in the piecewise affine form and use measurementsof the torque and the angular speed of the engine for computing the maximal set of observable states.This set, that is usually non-convex and disconnected, captures in a precise way how the main variablesand parameters of the driveline influence the possibility of estimating the shaft twist. Then, we showhow to exploit the knowledge of observable states in order to build computationally efficient deadbeatobservers for the reconstruction of the powertrain states.