New Features of P3$\delta$ software: Partial Pole Placement via Delay Action

This paper presents the software Partial Pole Placement via Delay Action, or P3$\delta$ for short. P3$\delta$ is a Python software with a friendly user interface for the design of parametric stabilizing feedback laws with time delays, thanks to two properties of the distribution of quasipolynomials' zeros, called multiplicity-induced-dominancy (MID) and coexisting real roots-induced-dominancy (CRRID). After recalling recent theoretical results on these properties and their use for the feedback stabilization of control systems operating under time delay, the paper presents the main features of the current version of P3$\delta$. We detail in particular its new features, such as the assignable admissible region (the set of allowable dominant roots and the corresponding delay), which helps the user in the choice of the input information, allowing a reliable stabilizing delayed feedback. We also present the newly set online version of P3$\delta$.