Sigma-Delta modulation sliding mode observers for linear systems subject to locally unstable inputs

In this article, we propose the use of a Sigma - Delta modulation approach combined with an appropriate dualization of generalized proportional integral (GPI) control strategies for the design of observers undergoing switched output injections, as in remote state estimation cases. The class of switched injection sliding observers inherit their robustness with respect to un-modeled 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 average extended output injections consist of linear combinations of a sufficient number of iterated integrals of the output estimation error. The proposed sliding mode observers have been shown to be useful in collision detection schemes for flexible robotics.