A quasicontinuous multivariable super‐twisting observer for 2n states systems with Lipschitz nonlinearities

Abstract

AbstractIn this article we present a global, finite‐time observer for continuous‐time nonlinear systems with states whose nonlinearities are characterized by a sufficiently small, globally Lipschitz constant. We consider the measurement of independent linear combinations of the system's states and assume that the system is subject to a class of external perturbations and/or an unknown input with a bounded norm for every time. To make use of this observer one requires the linear part of the plant to be observable. Furthermore, our design takes into account the linear part of the plant, instead of considering it as a perturbation in the observer's error dynamics. The observer is endowed with two correction terms: a Luenberger‐like gain and the nonlinearities of the generalized multivariable super‐twisting algorithm; and it is designed in the original plant's coordinates rather that designing it in a form obtained via the transformation of the state space. To finalize, we assess the observer performance via numerical simulations.