Are steady-state values in LTI systems differentially influenced by the rate an input is introduced?
Whenever the inputs to an LTI system stay constant for a time that is greater than the length of the impulse response, the system will reach the steady state for these inputs, regardless of history.

Whenever that is not the case, history matters. How the system reacts to different inputs is completely dependent on the system -- if you look at discrete time systems, [ 5 -5  0  0  0] will react differently than [ 1  1  1  1  1].

The first system will reach steady state after just two ticks, but produces fairly violent spikes on every input change:

[ 1  1  1  1  1  6  6  6  6  6 11 11 11 11 11] -&gt; [ 5  0  0  0  0 25  0  0  0  0 25 ...]
[ 1  2  3  4  5  6  7  8  9 10 11 12 13 14 15] -&gt; [ 5  5  5  5  5  5  5  5  5  5  5 ...]


The second takes five ticks, and smooths out steps of length 5:

[ 1  1  1  1  1  6  6  6  6  6 11 11 11 11 11] -&gt; [ 1  2  3  4  5 10 15 20 25 30 35 ...]
[ 1  2  3  4  5  6  7  8  9 10 11 12 13 14 15] -&gt; [ 1  3  6 10 15 20 25 30 35 40 45 ...]


You can see that apart from the start the outputs are the same (a ramp increasing by 5 each step).