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

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.