Direct Form 2 IIR filter input values
$x[k]$ is the input signal to the filter; it could be anything. There is no "rule" for what signal you can input to a linear filter. With that said, the stability of filters is usually talked about in a bounded-in, bounded-out (BIBO) sense. If the input signal is unbounded, then it's likely that the output signal will be also. So if anything, the "rule" that you're looking for would be to only apply signals $x[k]$ whose magnitude $|x[k]|$ is bounded below some value $B &lt; \infty$.