The proposed framework can be adapted to address other estimation problems, such as fault detection or parameter estimation, for nonlinear discrete-time systems by modifying the observer design objectives and constraints. For fault detection, the interval observer can be enhanced with residual generation mechanisms to detect deviations between the estimated state and the actual system behavior. By analyzing the residuals using fault detection algorithms, the observer can identify and isolate potential faults in the system. Similarly, for parameter estimation, the observer structure can be modified to estimate unknown parameters in the system dynamics. By incorporating parameter identification techniques into the observer design, the framework can be utilized to estimate and track the variations in system parameters over time, enhancing the overall estimation capabilities for nonlinear discrete-time systems.