Transient response of system with single pole $0 \le p < 1$ $G(z) = \frac{1-p}{z-p}$


  If the value of p satisfies $ 0 \leq p &lt; 1$ there are no oscillations
  in the transient response.


Question: Why is that $\uparrow$  true? I know roughly what a transient response is but how is the relation between the position of the pole and the nature of the transient response? 

Edit: In another paper by the same authors:


  Enforcing the stability of the controlled system means ensuring that
  the pole p is non-negative and less than 1.


Now I'm completely out, stability does not depend upon the position of the pole as long as they are inside the unit circle of the z-plane I have thought? 

Paper 2:

http://www.iste.uni-stuttgart.de/fileadmin/user_upload/iste/zss/publications/supplementaryMaterial/2014-ICSE-Control-PaperReviewCopy01.pdf

Look at the sentence short above eq. (10) on page 5

Paper 1 is not available on the internet as fas as I know. It's Antonio Filieri et al. "Software Engineering Meets Control Theory"
If you have a single real-valued pole, you get a term $k\,p^{(n-n_0)}u[n-n_0],n\ge 0$, with some constant $k$ and some delay $n_0\ge 0$ in the system's impulse response ($u[n]$ is the unit step). Clearly, if $|p|\ge 1$ the transient will never settle. If $-1&lt;p&lt;0$, the transient will alternate in sign (i.e., "oscillate"), like e.g.,

$$\left(-\frac12\right)^nu[n]=\left\{1,-\frac12,\frac14,-\frac18,\dots\right\}\tag{1}$$

So for a transient that decays (i.e., for the system to be stable) and that does not oscillate you need $0\le p&lt;1$.

Note that if you only have one real-valued pole $p$, stability implies $$-1&lt;p&lt;1\tag{2}$$ If you exclude systems with oscillating impulse responses (i.e., with a negative pole), you're left with the requirement $0\le p&lt;1$. But, as you've noticed, this requirement is not only dictated by stability (which only requires $(2)$), but also by the requirement of having no oscillations.