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Table 4 Computed r ’s of Example 2 for different values of τ with \(\pmb{\mu=0}\)

From: Improved results on reachable set bounding for linear systems with discrete and distributed delays

τ 0.1 0.3 0.5 0.7 0.9
[3] \(\sqrt{0.83}\) \(\sqrt{1.28}\) \(\sqrt{1.94}\) \(\sqrt {2.90}\) \(\sqrt{4.46}\)
[8] \(\sqrt{0.74}\) \(\sqrt{0.92}\) \(\sqrt{1.36}\) \(\sqrt {2.30}\) \(\sqrt{3.51}\)
[4] \(\sqrt{0.68}\) \(\sqrt{0.80}\) \(\sqrt{0.97}\) \(\sqrt {1.64}\) \(\sqrt{3.22}\)
[6] \(\sqrt{0.66}\) \(\sqrt{0.75}\) \(\sqrt{0.94}\) \(\sqrt {1.61}\) \(\sqrt{3.14}\)
[7] \(\sqrt{0.66}\) \(\sqrt{0.75}\) \(\sqrt{0.94}\) \(\sqrt {1.61}\) \(\sqrt{3.14}\)
[1] \(\sqrt{0.66}\) \(\sqrt{0.75}\) \(\sqrt{0.94}\) \(\sqrt {1.61}\) \(\sqrt{3.14}\)
Corollary 3.1 \(\sqrt{0.41}\) \(\sqrt{0.71}\) \(\sqrt{0.92}\) \(\sqrt {1.25}\) \(\sqrt{2.74}\)