The proposed interval observer design can be extended to handle time-varying nonlinear systems or systems with unknown disturbances by incorporating adaptive mechanisms into the observer framework. For time-varying systems, the observer parameters can be adjusted dynamically based on the changing dynamics of the system. This adaptation can be achieved by introducing time-varying gains or updating the observer structure based on real-time system measurements. Additionally, for systems with unknown disturbances, the observer can be augmented with robust estimation techniques to account for the uncertainties in the system. By incorporating adaptive and robust features into the observer design, the framework can effectively handle the complexities introduced by time-varying dynamics and unknown disturbances in nonlinear systems.