This chapter considers another approach to design unknown input observers for a class of time-delay systems as considered in Chap. 5. This approach is named an Expanded Dimensional Approach, where an auxiliary state vector \( \zeta (t) \equiv x(t-\tau )\) is augmented with the original state vector x(t) to form an expanded time-delay system. In its expanded dimensional form, we investigate two design approaches to design an unknown input observer. We show that the Expanded Dimensional Approach can overcome the condition imposed on matrix \(C_d\) as required in Chap. 5. To overcome this condition, it is necessary to use first-derivatives of two output measurements and a larger number of output measurements, i.e., \(p>2\) , and hence clearly a trade-off is required. Accordingly, we obtain a disturbance-free time-delay system, and the unknown input can be asymptotically estimated by designing a generalized functional observer.