A class of adaptive robust state observers with simpler structure for uncertain non-linear systems with time-varying delays

The problem of adaptive robust state observer design is considered for a class of uncertain non-linear dynamical systems with multiple time-varying delays. It is assumed that the upper bounds of the non-linear delayed state perturbations are unknown and that the time-varying delays are any non-negative continuous and bounded functions, which do not require that their derivatives have to be less than one. In particular, it is only required that the non-linear uncertainties, which can also include time-varying delays, are bounded in any non-negative non-linear functions, which are not required to be known for the system designer. For such a class of uncertain non-linear time-delay systems, a new method is presented whereby a class of memoryless adaptive robust state observers with a rather simpler structure is proposed. 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 be guaranteed to be uniformly exponentially convergent towards a ball, which can be as small as desired, in the presence of significant uncertainties and time delays. Finally, a numerical example is given to demonstrate the validity of the results.