Proper transfer function

Proper in control theory

Proper denotes a transfer function where the degree of the nominator does not exceed the degree of the denominator.

The following transfer function is 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\leq deg({\textbf {D}}(s))=4

.