Memoryless adaptive robust asymptotic state observers for a class of nonlinear time-delay systems

In this study, the problem of memoryless adaptive robust state observer design is considered for a class of uncertain nonlinear time-delay systems. It is supposed that the upper bounds of the uncertainties, including delayed states, are assumed to be unknown. An improved adaptation law with sigma-modification is employed to estimate such unknown bounds. Then, by making use of the updated values of these unknown bounds, a class of memoryless adaptive robust state observers is proposed for uncertain nonlinear time-delay systems. It is also shown that by employing the proposed adaptive robust state observer, the observation error between the observer state estimate and the true state can converge asymptotically to zero in the presence of significant uncertainties and time delays. Finally, a numerical example is given to demonstrate the validity of the results.