Convex handling of nonlinear nominal models can overcome limitations on sliding mode observer design

Abstract

This report establishes that overcoming limitations on standard synthesis of sliding mode observers, namely, the rank and size requisites for output/perturbation decoupling and the number of transformations required, depends on avoiding linear nominal systems. This task is achieved by two local diffeomorphisms which transform the system into a flexible nonlinear nominal structure plus disturbances. Based on such decomposition, convex modelling and optimization is employed to design the continuous part of the observer while the discontinuous one is adequately chosen to guarantee sliding over a nonlinear output error surface. Examples, both academic and physical, that cannot be treated by the standard methodology, are presented to illustrate the advantages of the proposal.