Robust least-fragile PI controller design for a coupled-tanks system with uncertain time-varying input time-delay

PID control is a widely used methodology in many industrial applications, particularly for processes with input-output delays. For these processes, it is well known that significant delays cause poor performance, and it is important to better understand their effects on the dynamic behavior of the closed-loop system. Furthermore, these delays can be uncertain and time-varying. In this work, we present a robust and least-fragile PI controller design for uncertain time-varying delays. In particular, we will explicitly construct such controllers for a class of delay systems modeling a coupled tank system.