Computing Control Invariant Sets for Waiting-Time Switched Systems: A Study Case of Glucose Regulation

Waiting-time constraints, bounding the minimum and maximum time of permanence in a given mode of a switched system, can be included in optimization-based control formulations by means of hard constraints. However, basic concepts such as equilibrium and invariance sets are modified by these constraints affecting the formal stability analysis as well. This letter explores general regions of the state space wherein switched system trajectories under waiting-time constraints can feasibly (and indefinitely) remain inside, replacing the concept of invariance with those of permanence. Explicit algorithms to compute these regions inside an (out of the origin) target window are provided, while the glucose regulation problem for Type 1 Diabetes Mellitus (T1DM) patients is considered as an example to highlight its main properties.