Limit 2-Cycles for a Discrete-Time Bang-Bang Control Model

Table 7

0=max{𝜉⁻₀,𝜉⁻₁}=𝜉⁻₀>𝜉⁻₁.

𝑦−1	𝑧−1	Condition	Condition	lim𝑛(𝑦𝑛,𝑧𝑛)
∈𝑅^+	∈𝐑			(𝜉^+0,𝜉^−1)
∈𝑅^−	∈𝑅^+		𝜉^+1≥0	(𝜉^−0,𝜉^+1)
			𝜉^+1<0	(𝜉^+0,𝜉^−1)
∈𝑅^−	∈𝑅^−		𝜉^+1≤0	(𝜉^+0,𝜉^−1)
∈(𝐴^+0,𝑘+1,𝐴^+0,𝑘]⊂𝑅^−	∈(𝐴^+1,𝑠+1,𝐴^+1,𝑠]⊂𝑅^−	0≤𝑘≤𝑠	𝜉^+1>0	(𝜉^+0,𝜉^−1)
∈(𝐴^+0,𝑘+1,𝐴^+0,𝑘]⊂𝑅^−	∈(𝐴^+1,𝑠+1,𝐴^+1,𝑠]⊂𝑅^−	0≤𝑠<𝑘	𝜉^+1>0	(𝜉^−0,𝜉^+1)