Robust Σ–Δ modulation-based sliding mode observers for linear systems subject to time polynomial inputs

Abstract

In this article, we propose the use of Σ–Δ modulation-based sliding mode observers undergoing switched output injections as in remote state estimation cases. The class of switched observers, treated here, inherit their robustness with respect to un-modelled classical perturbation inputs of the polynomial type affecting the observed plant, from that of an average (non-discontinuous) observer design exhibiting dynamic output reconstruction error injections. These extended output injections consist of linear combinations of a sufficient number of iterated integrals of the output estimation error. In achieving the required robustness behaviour with respect to classical perturbations, a suitable and natural dualisation of Generalised Proportional Integral control is being used. The proposed observers are shown to be useful in collision detection schemes for flexible robotics.