The understanding of invariant set theory is essential in the design of controllers for constrained systems. This paper presents some concepts related with the invariant set theory and Set-Based Model Predictive Control (set-based MPC). Precisely, introduces a new class of sets from where the closed-loop system reaches a target set before a pre-established number of steps. These novel concepts are based on several results presented in a former work [1]. The main results are exposed in a theoretical context, however several simulation examples show its potential and properties
