Observer design is a research area in the field of control theory, specifically focusing on the development of mathematical algorithms that can estimate the internal states of a system using only its input and output data. This is particularly important in systems where not all states are directly measurable, such as in complex systems or systems with noisy measurements. Observers typically use a mathematical model of the system, along with sensor data, to estimate the internal states of the system in real-time. This estimation can then be used for various purposes, such as control, monitoring, fault detection, or system identification. Overall, observer design plays a crucial role in control systems engineering by allowing for accurate estimation of a system's internal states, even when direct measurements are not available.