An observer for a class of nonlinear systems with multiple state and measurement delays: A differential geometry-based approach

摘要

This paper presents an observer for a class of nonlinear systems, suitably affine in the input and the delayed terms, with constant, known, and arbitrarily large time-delays in both internal and output variables. It is assumed that the system at hand is globally drift-observable and that the function describing the dynamics is globally Lipschitz. Moreover, it is assumed that the system at hand admits full uniform observation relative degree. A differential geometry-based approach is followed. The well-known chain procedure is employed in order to deal with arbitrarily large output delay. It is proved that, for any given delays at states and output, there exist a suitable gain matrix and a Hurwitz matrix, involved in the observer algorithm, such that, when a sufficiently large number of chain elements are employed, the observation error converges asymptotically to zero. The effectiveness of the proposed method is illustrated by numerical examples. (c) 2020 European Control Association. Published by Elsevier Ltd. All rights reserved.