Also, the integral of the real part of a strictly proper transfer function is zero.

The strictly proper transfer function can then be transformed into a canonical state space realization using techniques shown above.

A proper transfer function will never grow unbounded as the frequency approaches infinity:

A strictly proper transfer function is a transfer function where the degree of the numerator is less than the degree of the denominator.

In control theory, a proper transfer function is a transfer function in which the degree of the numerator does not exceed the degree of the denominator.