This is due to the fact that our main application domain is the AC motor where the derivative of the input does not exist or is not easy to obtain. This appears, when we consider the converter in the observer of SMC .
Observers are designed to estimate unknown states whereas control action is considered to enable the system to meet design specifications. Those concepts are the same for SMC-based designs.
It's correct you said sliding observer control works as fuzzy sliding mode controller or adaptive sliding mode controller? and I'd like to know about the difference between observer and adaptive in application?