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Test whether the following functions are positive real function $$ \begin{aligned} &\text { i) } F(s)=\frac{s^3+6 s^2+7 s+3}{s^2+2 s+1} \\ \end{aligned} $$
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written 19 months ago by
prajapatijaimin
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Solution:
$ \begin{gathered} \text { i) } F(s)=\frac{s^3+6 s^2+7 s+3}{s^2+2 s+1}=\frac{N(s)}{D(s)}....(1) \\\\ N(s)=s^3+6 s^2+7 s+3 \end{gathered} $
$ \begin{aligned} \\ &\begin{array}{c|c} s^3 & 1 \\\\ \hline s^2 & 6 \\\\ \hline s^1 & \frac{13}{2} \\\\ \hline s^0 & 3 \\\\ \end{array}\\\\ &N(S) \text { is Hurwitz's polynomial } \end{aligned} $ …
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