Design of Adaptive Robust State Observers with Simpler Structure for a Class of Uncertain Time–-Delay Systems

The problem of adaptive robust state observer design is considered for a class of uncertain nonlinear dynamical systems with multiple time–varying delays. In the paper, it is only required that the nonlinear uncertainties, which can also include time–varying delays, are bounded in any nonnegative nonlinear functions which are not required to be known for the system designer. 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. Finally, a numerical example is given to demonstrate the validity of the results.