The Luenberger observer is useful to estimate the non-measurable state variables of a dynamic system. The controller is normally a LQR (linear quadratic regulator). In order to use it the system has to be observable. A  DC DC boost converter is a kind of hybrid system (switched system, switching control) that need a special type of control. Therefore, hybrid observability and hybrid control are important key words. Please have a look at the following references:

1) Bemporad A., Ferrari-Trecate G., Morari M.: Observability and controllability of piecewise affine and hybrid systems. IEEE Trans A.C. 45, 1864–1876 (2000)

2) Geyer T. Papafotiou G., Morari M.: Hybrid model predictive control of the step-down DC–DC converter. IEEE Trans. Control Syst. Technol. 16(6), 1112–1124 (2008)

3) Iannelli L., Johansson K.H., Jönsson U.T., Vasca F.: Subtleties in the averaging of a class of hybrid systems with applications to power converters. Control Eng. Pract. 16, 961–975 (2008).

4) Kamri, D., Larbes, C., Observer-Based Control for DC–DC Converters. Practical Switching Control. Arabian Journal for Science and Engineering, Vol 39, No 5, pp 4089–4102, May 2014.

The observer will not serve (used) to control.

I not understand your question, but if you want to control your system using full state feedback , normally you need to design a observer (Kalman filter , Luenberger observer,etc).  Maybe you want to control the DC DC boost converter using Pole placement method that is similar to the approach of Luenberger observer.

Also if you have problems as steady state error you can include integral action to your controllers.

Yeah, the observer won't control but it will keep a check on the steady state errors and i am doing predictive control so pole placement is not an option sir.

Please refer to these articles:

https://www.researchgate.net/publication/313576646_From_PID_to_Nonlinear_State_Error_Feedback_Controller

https://www.researchgate.net/publication/312046377_Improved_Sliding_Mode_Nonlinear_Extended_State_Observer_based_Active_Disturbance_Rejection_Control_for_Uncertain_Systems_with_Unknown_Total_Disturbance

https://www.researchgate.net/publication/309655805_On_the_Improved_Nonlinear_Tracking_Differentiator_based_Nonlinear_PID_Controller_Design

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