TABLE 9.

Bounds for the Dimensionless Variables

Nonsingular variable	Singular variable
0 ⩽ u1 ⩽ 1	$0⩽v_1⩽\text{min}\left(\frac{k_{-2}+k_3}{k_2{\left[{\text{R}}_{\text{s}}\right]}_T},\frac{k_{-2}+k_3}{k_2{\left[{\text{G}}_{\text{s}}\right]}_T}\right)$
0 ⩽ u2 ⩽ 1	0 ⩽ v2 ⩽ k6[Gs]T/k5
0 ⩽ u3 ⩽ min(l, [Gs]T/[UC]T)	$0⩽v_3⩽\text{min}\left(\frac{h_{-2}+h_3}{h_2{\left[{\text{R}}_{\text{i}}\right]}_T},\frac{h_{-2}+h_3}{h_2{\left[{\text{G}}_{\text{i}}\right]}_T}\right)$
0 ⩽ u4 ⩽ 1	0 ⩽ v4 ⩽ h7[Gi]T/h5
0 ⩽ u5 ⩽ 1	$0⩽v_5⩽\text{min}\left(\frac{l_{-1}+l_2}{l_1},\frac{\left(l_{-1}+l_2\right){\left[{\text{G}}_{\text{s}}\right]}_T}{l_1{[\text{UC}]}_T}\right)$
0 ⩽ u6 ⩽ min(l,[Gi]T/[Rs]T)	0 ⩽ v6 ⩽ (l−3 + l4)/l3[iPDE]T
0 ⩽ u7 ⩽ ∞	$0⩽u_8^{*}⩽\infty$