Being able to directly measure the states just means that you don't need to estimate the states. So this is a good situation!

In both cases you would design a gain vector K , to place the closed-loop poles (i.e. of the system with state feedback) at the desired place in the complex s or z plane (depending on whether you are designing a continuous- or discrete-time controller). Do this using Ackerman's method, for instance.  

In the latter, case you would also need to design an observer to estimate the states -e.g. a Luenberger observer. This design process would involve the design of a gain vector L, to place the poles of the observer (to obtain the desired transient and noise filtering properties).   

Have a look at "Linear State-Space Control Systems" by Robert L. Williams II and Douglas A. Lawrence for a very good introduction (continuous-time only).

It seems you have more than 4 state variables. So you need to estimate the remaining state variables using Luenberger observer  as mentioned by Hugh. 

I think if the the control law needs the access to some unmeasured states you need to estimate them using observers or approximation techniques , so it depends on your control law and the system... i guess .

Search for "Differential flatness theory" or "Flatness-based control" that will help you to easily design a controller for your nonlinear system.

If the unmeasured states are stable, then yes you can use state feedback controller to stabalize the unstable measured states. If some unmeasured states are not stable, then you have to used either full or reduced order observer... kalman filter is another option but more advanced and complex...

Good luck

Thanks All for the responses.

I am sorry, I was not  clear.

The problem in hand is that we can't use any estimator, only by using some measures states, we need to stabilize the system or improve the performance.

Consider the present case as measured states are the output of the systems and we need to design output feedback control, may it be static or dynamic.

anyway, Thanks again for your time.

I think you need to do either Input/Output feedback linearization or Input/State feedback linearization and that depends weather your system has internal dynamics or not. It means that if the relative degree is less then the order of the system then you internal dynamics in your system and you need I/O feedback linearization. You will feedback only the normal dynamics (linear dynamics) and for the internal dynamics (nonlinear synamics) , which is the nonlinear part, you have to proof the stability using Lyapunov stability theorem and then you don't need to takes those states as feedback.