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(Solved): 1. Determine whether the function F(s)= realizable. S +55 +9s+3/S +4s +7s+9 is a positive re ...



1. Determine whether the function F(s)= realizable. S³ +55³ +9s+3/S³ +4s³ +7s+9 is a positive real functions (PRF) and hence [4 Marks]

1. Determine whether the function \( \mathrm{F}(\mathrm{s})=\frac{s^{3}+5 s^{3}+9 s+3}{s^{3}+4 s^{3}+7 s+9} \) is a positive
1. Determine whether the function is a positive real functions (PRF) and hence realizable. [4 Marks]


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The function F(s) is a positive real function (PRF) if and only if all of its poles lie in the left half-plane.
The poles of F(s) are the roots of the denominator polynomial


Poles of the transfer function: To find the poles, we set the denominator equal to zero and solve for s:
  
Combining like terms, we get:

  
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