Figure 3.

Domain in (x₁, x₂) plane. (A) Region where γ changes sign. We see that inside the triangular region x₁ + x₂ ≤ 1 of the first quadrant, γ changes sign only along the line ax₁ + bx₂ − c = 0. For this line to be interior to Ω_c as depicted, we must be in the parameter regime indicated in (49). X and Y vector fields corresponding to vertices of control set U. For singular controls to lie in U, X and Y must point to opposite sides along $\mathcal{L}$. (B) Same as in (A), but with α = 0.