An observer for a class of nonlinear systems with multiple state and measurement delays: A differential geometry-based approach. (November 2020)

• Record Type: Journal Article
• Authors: Talebi, Soroush; Ataei, Mohammad; Pepe, Pierdomenico
• Is Part Of: European journal of control. Volume 56(2020)
• Page Start: 132
• Page End: 141
• Publication Date: 2020-11
• Subjects: Nonlinear Observers -- Time delay systems -- State delay -- Output delay; Control theory -- Periodicals; Automatic control -- Periodicals; Automatic control -- Mathematics -- Periodicals; Electronic journals; 629.805
• DOI: 10.1016/j.ejcon.2020.02.010
• Languages: English
• ISSNs: 0947-3580

Abstract

Abstract: 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.