Differentiable Families of Planar Bimodal Linear Control Systems

Table 1

𝒮-Invariant numbers.

	Hypotheses	Numbers	Properties
(1)		Δ0,𝑏1	𝑎3=0
(2)	𝑏1=0		𝑏2=0
(3)	𝑎3=0	𝑎1,𝛾1,𝑎4	Δ12=0,Δ1=0,Δ2=0
(3′)	𝑎3=0,Δ12≠0	Δ1/Δ12,Δ2/Δ12
(4)	𝑎3=0,𝑎1=𝑎4		𝑎2=0
(4′)	𝑎3=0,𝛾1=𝑎4		𝛾2=0
(5)	𝑏1=0,𝑎3=0,𝑎1=𝑎4	𝑏2/𝑎2
(5′)	𝑏1=0,𝑎3=0,𝛾1=𝑎4	𝑏2/𝛾2