I have read about state space model and MAMBA. The state space model is described as:
$\dot{h}(t) = Ah(t) + Bu(t)$
$y(t) = Ch(t) + Du(t)$
Then the discretization is:
$\bar{A} = exp(\Delta A)$
$\bar{B} = (\Delta A)^{-1}(exp(\Delta A) - I)\Delta B$
From my understanding, $\Delta$ is small change over time i.e $dt$, and $t$ is just a scalar represent time. However, in state space model S4 and Mamba paper, they use $\Delta$ as a high dimensional matrix, which cause confusion to me. How can I understand this $\Delta$?
