Don't bid high for this project because if you are familiar with this it is very easy to do.
I attached some pdf files and a word document as a project description for the system you will use.
First, in the document named Science you’ll find the same project requirements (They designed a state feedback controller and an observer based controller) BUT they used a model where the delay is present only in the state and not on the input as well and they used a saturated input, I don’t know what approximation they used to not use the delay in the input (so you will not use this model but it is very interesting to read this article because it present the application very well).
In the article named On Designing Lyapunov-Krasovskii Based AQM for Routers
Supporting TCP Flows you will find the system that you will use, a linear time delay system with a constant delay in input and state. In this article they studied the independent of delay case and the dependent of delay case, and they studied the case where the delay is uncertain by using polytopic uncertain model but they didn’t consider the observer based controller. Finally they did a comparison with the results obtained using a PI controller designed in the article Analysis and design of controllers……. (you will use the same numerical values as those on these 2 artciles).
So, what will you do is:
-Use the system model described in the article on designing Lyapunov-Krasovskii Based AQMs…..
-1- Assume all the states are available, design a state feedback controller by finding the gain K using LMI techniques issued from Lyapunov Krasovskii theory (It is done in the article on designing Lyapunov-Krasovskii Based AQMs….. but you should explain the passage from the case where u=0 to the LMI for u=Kx and how to resolve this LMI using Matlab and finding the corresponding positive definte matrices then the gaing K , you should explain things very clearly here because it is the key of the project).
You should do this for the independent of delay case (If you can do the dependent of delay case too it will be great)
-2- Assume now that the states are not available, so you should design a an Observer Based Controller using LMI as well by finding the gain K and L of the observer (Explain the LMI with references (you should have knowledge of time delay systems) and how to solve them using Matlab)
-3- Do some comparisons with the PI controller designed on Analysis and design of controllers……. As done in the article On Designing Lyapunov-Krasovskii Based AQM for Routers
Supporting TCP Flows (with the same numerical values), you will focus on the queue length.
-4- Facultative: If you can do the Polytopic approach as done in the article as well it would be great (it is not a must but if you can do it and it is easy for you just go head)
Hope everything is clear. If you have any questions just let me know.