Proper Transfer Function

A proper system has the following properties

$$h(s)=\frac{n(s)}{d(s)}\to deg(d(s))\ge deg(n(s))$$

and

$$|h_p(j\infty )|<\infty ,\cap |h_{sp}(j\infty )|=0$$

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For example:

$$\begin{array}{rl}G(s)& =\frac{s+2}{s-3}\\ G_{\infty }& =\underset{\omega \to \infty }{\lim }|G(jw)|=1\end{array}$$