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== Proper in control theory ==
'''Proper''' denotes a [[transfer function]] where the degree of the nominator does not exceed the degree of the denominator.
=== Example ===
The following transfer function is '''proper'''
:<math> \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}}</math>
because
:<math> deg(\textbf{N}(s)) = 4 \leq deg(\textbf{D}(s)) = 4 </math>.
The following transfer function however, is '''not proper'''
:<math> \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}}{d_{1}s^{3} + d_{2}s^{2} + d_{3}s + d_{4}}</math>
because
:<math> deg(\textbf{N}(s)) = 4 \nleq deg(\textbf{D}(s)) = 3 </math>.
=== Implications ===
A proper transfer function will never grow unbounded as the frequency approaces infinity.
:<math> |\textbf{G}(\infty)| < \infty </math>
=== Related ===
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