Interval estimation for discrete-time linear time-delay systems based on state augmentation

This paper investigates an interval estimation method for discrete-time linear time-delay systems subject to unknown but bounded disturbances and noise. We utilize the state augmentation technique to decouple the time delays. The interval estimation problem for the time-delay system will be transformed into that for a delay-free state augmented system. We then propose a two-step method which consists of robust observer design and zonotope-based interval analysis to achieve interval estimation. In observer design, a T−N−L observer is used to provide more degrees of design freedom, whose robustness is characterized by H_∞ performance. Finally, a numerical example is provided to demonstrate the effectiveness and superiority of the proposed method.