Koga's multivariable stability criterion

It is shown that a multivariable polynomial P(p;µ
1
, µ
2
,...,µ
s
) is nonzero in Re p > 0, Re µ
1
> 0,..., Re µ
s
> 0 if and only if P(p; 1, 1,..., 1) ≠ 0 and P(p; tanh τ
1
p, tanh τ
2
p,..., tanh τ
s
p) ≠ 0 in Re p > 0 for all τ
1
> 0, τ
2
> 0,..., τ
s
> 0.