Stubborn State Estimation for Delayed Neural Networks Using Saturating Output Errors

This paper is concerned with the stubborn state estimation of delayed neural networks that subject to a general class of disturbances in measurements, including outliers and impulsive disturbances as its special cases. This class of disturbances may be unbounded, irregular, and assorted; therefore, they can hardly be suppressed by existing identification-based estimation approaches. In this paper, a stubborn state estimator is constructed by intentionally devising a saturation scheme on the injection of output estimation error. The embedded saturation can effectively resist the influences from these measurement disturbances by saturating them. Moreover, the saturation threshold in the designed scheme is not constant but governed by a dynamic equation with parameters to be designed. Benefiting from this adaptiveness, the estimator obtains more freedom in dealing with various disturbances. By combining a novel Lyapunov functional, the generalized sector condition and two latest integral inequalities, a delay-dependent criterion is derived in a less conservative way to check whether the estimation error system with this dynamic saturation is globally stable. A sufficient condition with two tuning scalars is further provided to codesign the gain of the state estimator and the evolution law of the saturation threshold. Finally, two numerical examples are used to illustrate the stubbornness of this state estimator in the presence of measurement outliers or impulsive disturbances.