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

Table 5

0=min{𝜉⁺₀,𝜉⁺₁}=𝜉⁺₁<𝜉⁺₀.

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