Practical implementation of state observer
Couldn't be simpler: For example you power the device with mains power (output) and you measure the current/voltage with a DMM (observer).
EDIT:



simulate this circuit &ndash; Schematic created using CircuitLab
@ShiS Current/Voltage is just an example, the controller outputs a value let's say u(t) and gets a feedback value, let's say y(t). The observer's input values are both u(t) and y(t).
The signals can be routed inside the controller, where both control and observer are implemented, y(t) is measured with ADC and u(t) is output to DAC.
If the observer is a different black box, then it can have two ADCs to measure y(t) and u(t), then those values have to be normalized, to have the same units as controller.
The observer can also have no measurement ADC, the signals u(t) and y(t) could be sent from the controller to the observer via a communication link.
If this observer is an analog computing device, then it can simply buffer the u(t) and y(t) with an opamp.