Help needed in my control research hobby project.

LMI control for a robot that can balance itself.
Create equations for the state space of self-balancing robots. Based on the equations, develop a PID algorithm, then simulate it in Matlab. Orientation angle, step response, steady state error, and tracking are among the parameters that need to be examined.
The self-balancing robot's LMI (Linear Matrix Inequality) control algorithm will then be developed in Matlab and tested using the same test parameters. Verify that LMI is a superior control method for self-balancing robots than PID. Considering that I already have the physical robot on my end, the candidate should be able to link Matlab with an Arduino. Results will include both physical and Matlab simulation data. It would be extremely appreciated if the project could be finished in one month.