when can we prove convergence of observer and controller seperately

xsro

Hi, we as a research group in Sun Yat-sen University are exploring the hierarchy design of observer-controller architecture.

In many papers on observer-based output feedback control, people usually design the observer and the state feedback controller separately. More precisely, they analyze the convergence of the state observer and then prove the convergence of the closed-loop system under the state feedback. Certainly, mostly it works and the simulations perform well. But, in this way, the output feedback design makes no sense, and the result is trivial or even not convincing.

xsro

In many papers on finite-time controllers, two parts are usually designed as follows:

A finite-time observer.
A state-feedback controller.

The proof process is usually like this:

First, prove the finite convergence of the observer within a finite time .
Then, analyze the system for the time .

This is a common approach, yet my professor doesn't approve of it. I know that this approach is rather simplistic and lacks sophistication. But is it necessary to analyze the entire system? And is it feasible to do so?