Forward Invariance

Definition

The property that system trajectories remain within a viable region S ⊆ X for all time. Forward invariance ensures the system never evolves into failure states—if x₀ ∈ S, then xₜ ∈ S for all t ≥ 0. This is the first prerequisite for regeneration.

Formula

Example

A hospital's forward invariance means equipment ages, staffing levels, and maintenance thresholds always remain within clinically safe bounds—the system architecture prevents collapse into failure states.

Source

FRS Section 3.1