Disturbance observer for uncertain Lipschitz nonlinear systems under multiple time-varying delays

The prime aim of this paper is to synthesize a novel disturbance observer based on a cascade structure for a class of Lipschitz nonlinear systems with model uncertainties and output measurements corrupted by external disturbances and multiple time-varying delays. The proposed observation scheme is comprised of a cascade of state observers, where everyone is tasked to estimate the state over a short time interval, while the initial item provides the undelayed estimation. Each item of the cascade disturbance observer contains a dynamical proportional-integral term which allows to reduce effects of the time-delay and the unknown signals. An originality of the proposed approach is that it involves less-restrictive Lipschitz inequalities for function describing the nonlinear system. The convergence analysis is based on a Lyapunov–Krasovskii functional approach to demonstrate that the observation error is decaying to zero. The proposed disturbance observer can appropriately estimate the state variables by attenuating the effect of model uncertainties and external disturbances. An example considering a Chua’s chaotic system illustrates the effectiveness of the proposed approach.