Theorem G — Door Stability

Prerequisites: Theorem B (door finiteness), perturbation analysis (Chapter 6).

Theorem G. (Complete proof in Chapter 6, Theorem G.)

Under perturbation $\Vert \delta W{\Vert }_{\infty }$, setting $ϵ=|V|\cdot \Vert \delta W{\Vert }_{\infty }$:

(i) $|b^{\prime }-b|\le |V|\cdot \Vert \delta W{\Vert }_{\infty }$. (ii)--(iv) Doors with margin $>ϵ$ are stable; only the $ϵ$-boundary layer may change.