Why is it difficult to measure every part of a state vector exactly and instantly?

In the context of control theory, it is considered unrealistic to assume that every component of a state vector can be measured exactly and instantaneously because physical systems and their environments are subject to complexities that prevent perfect, real-time data acquisition.1

Because of these practical limitations, control theory must often be broadened to include the task of state determination, which is a central focus of statistical prediction and filtering theory. Rather than relying on direct, instantaneous measurements, engineers typically implement a two-step process to manage this challenge:1

• State Estimation: An optimal filter, such as a Kalman filter, is used to calculate the best possible estimate of the present state vector based on available, imperfect data.1
• Control Implementation: An optimal control law is then applied using this estimated state vector to determine the necessary control actions.1

This approach allows for effective control even when the internal state of a system cannot be perfectly observed at every moment.1