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Theory and Modern Applications

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

\(\sqrt{0.41}\)

\(\sqrt{0.71}\)

\(\sqrt{0.92}\)

\(\sqrt {1.25}\)

\(\sqrt{2.74}\)