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Theory and Modern Applications

Table 2 Computed r ’s of Example 1 for different values of τ with \(\pmb{\sigma=0.1}\) , \(\pmb{\mu=0.5}\)

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

[1]

\(\sqrt{9.3269}\)

\(\sqrt{9.5769}\)

\(\sqrt{9.8531}\)

\(\sqrt{10.1593}\)

\(\sqrt{10.5000}\)

[2]

\(\sqrt{5.5456}\)

\(\sqrt{5.7058}\)

\(\sqrt{5.9109}\)

\(\sqrt {6.1423}\)

\(\sqrt{6.4505}\)

Theorem 3.1

\(\sqrt{3.0762}\)

\(\sqrt{3.9978}\)

\(\sqrt{4.1181}\)

\(\sqrt{4.4765}\)

\(\sqrt{5.0025}\)