Strictly proper

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In control theory, a strictly proper transfer function is a transfer function where the degree of the numerator is less than the degree of the denominator.

[edit] Example

The following transfer function is not strictly proper

$\textbf{G}(s) = \frac{\textbf{N}(s)}{\textbf{D}(s)} = \frac{s^{4} + n_{1}s^{3} + n_{2}s^{2} + n_{3}s + n_{4}}{s^{4} + d_{1}s^{3} + d_{2}s^{2} + d_{3}s + d_{4}}$

because

$deg(\textbf{N}(s)) = 4 \nless deg(\textbf{D}(s)) = 4$ .

The following transfer function however, is strictly proper

$\textbf{G}(s) = \frac{\textbf{N}(s)}{\textbf{D}(s)} = \frac{n_{1}s^{3} + n_{2}s^{2} + n_{3}s + n_{4}}{s^{4} + d_{1}s^{3} + d_{2}s^{2} + d_{3}s + d_{4}}$