The project is still under development and the next updates will focus on the following tasks:

• Comparing different cenarios for stability of PI-Controlled first order processes: constant time-delay ❌ time-varying time-delay
• For the Skogestad-IMC PI Controller proposed in "Simple analytic rules for model reduction and PID controller tuning", 2003, Skogestad, verifying what's the worst cenario for the stability of the PI-Controlled closed-loop system: constant time-delay or time-varying time-delay in a first order model
• Computationally Analysing the stability in the frequency domain for better understanding what's the worst situation for a PI-Controlled first order process: given (Kp,Ki), what it is the maximum constant time-delay for the system to hold stability? what it is the maximum magnitude for the time-varying for the system to hold stability?
• Using the LMI Approach to verify stability conditions for time-varying delay systems (Lyapunov-Krasovskii and Razumikhin);
• Analysing the stability in the time domain (Lyapunov-Krasovskii, Razumikhin...) to find less conservative conditions to tell what's the worst case time-delay for a PI-Controlled first order process
• Testing the theoretical results in a intensive care unit in order to verify the stability conditions proposed