\begin{rmk}
 The LMI for Discrete-Time Uncertain Peak Estimation is similar to LMI \eqref{eq:peak_lmi_un} in continuous time. If time is not included, support constraints \eqref{eq:peak_lmi_un_time}-\eqref{eq:peak_lmi_un_time2} are unnecessary. The Liouville operator $\textrm{Liou}_{\alpha \gamma}(y^0, y^p, y^k)$ is now the affine relation in moments  induced from Liouville's Equation \eqref{eq:peak_meas_un_disc_flow}  for every test function $v(x, \theta) = x^\alpha \theta^\gamma$,
 \begin{align}
 \label{eq:liou_disc_lmi_unc}
    0&= \inp{x^\alpha \theta^\gamma}{ \delta_0 \otimes \mu_0} - \inp{x^\alpha  \theta^\gamma}{\mu_p} \\
    &+ \textstyle \sum_k\inp{( f_{k}(x, \theta, w)^\alpha \theta^\gamma - x^\alpha \theta^\gamma}{\mu_k}. \nonumber
\end{align}
 \end{rmk}
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