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The Laplace transform of a causal signal y(t) is \(y\left( s \right) = \frac{{s + 2}}{{s + 6}}\). The value of the signal y(t) at t = 0.1s is ______ units.

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\(\begin{array}{l} y\left( s \right) = \frac{{s + 2}}{{s + 6}}\\ y\left( s \right) = \frac{{s + 2 + 4 - 4}}{{s + 6}}\\ = 1 - \frac{4}{{s + 6}} \end{array}\)

Apply inverse Laplace transform,

⇒ y(t) = δ(t) - 4e-6t 4(t)

At,

t = 0.1

⇒ y(0.1) = δ(0.1) - 4e-6(0.1) u(0.1)

= 0 - 4e-0.6 = -2.195

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