Cascade observer design for a class of uncertain nonlinear systems with delayed outputs

This paper proposes a state observer with a cascade structure for a class of nonlinear systems in the presence of uncertainties in the state equations and an arbitrarily long delay in the outputs. The design of the observer is achieved under an appropriate set of assumptions allowing to establish the ultimate boundedness of the observation error. Indeed, a suitable expression of the asymptotic observation error, involving the delay, the bound of the uncertainties and the Lipschitz constant of the system nonlinearities, is derived. Besides, it is shown that this ultimate bound is a decreasing function of the cascade length and is equal to zero in the uncertainty-free case. The observer design is first carried out in the case where the output measurements are continuously available and subsequently extended to the case where the outputs are available only at (non equally spaced) sampling instants. The performance of the proposed observer and its main properties are highlighted through illustrative simulation results involving an academic example. (C) 2017 Elsevier Ltd. All rights reserved.