This paper introduces a new class of delay-based proportional integral (PI) control schemes, referred to as the proportional delayed integral (P \(\delta \) I) controller. This novel approach incorporates an intentional delay into the control scheme, introducing a new tuning parameter (the delay) that enhances the system’s response while preserving the zero steady-state error property of the classical PI controller. To determine an appropriate tuning, we adopt a geometric approach that serves two purposes: first, it provides an analytical method to ensure the closed-loop stability of the system; second, it enables the optimization of the spectral abscissa with respect to the delay parameter. Furthermore, the robustness of the proposed controller against parameter uncertainties is analyzed and optimized. Several numerical examples demonstrate the effectiveness of the proposed method, and an experimental implementation using a DC–DC boost converter underscores the controller’s practical relevance.
