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The general process in the discrete-time linear time-invariant (DLTI) direct feedthrough state-space model form is considered:

\begin{equation} \begin{cases} \boldsymbol{x}(k+1) = \boldsymbol{A} \boldsymbol{x}(k) + \boldsymbol{B} \boldsymbol{u}(k), \\ \boldsymbol{y}(k) = \boldsymbol{C} \boldsymbol{x}(k) + \boldsymbol{D} \boldsymbol{u}(k). \end{cases} \label{eq:DLTI} \end{equation}

For the DLTI system, the following set is defined such that $\boldsymbol{x}_k \in \mathcal{X}$, $\boldsymbol{y}_k \in \mathcal{Y}$, $k=0,1,\dots,N-1$:

\begin{equation} \mathcal{S} = \Bigg\{ \{ \boldsymbol{x}_0, \boldsymbol{u}_0,\boldsymbol{u}_1,\dots,\boldsymbol{u}_{N-1} \} :\ \mathbf{H} \boldsymbol{x}_0 + \mathbf{L}_0 \boldsymbol{u}_0 + \mathbf{L}_1 \boldsymbol{u}_1 + \dots + \mathbf{L}_{N-1} \boldsymbol{u}_{N-1} \leq \mathbf{K} \Bigg\}. \label{poly:safeSetapprox} \end{equation}

What is the official name for the set $\mathcal{S}$ that are used in the literature?

ConT
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    Call it whatever you want to call it as long as it makes sense in the context you are considering it. – KBS Mar 23 '23 at 17:05
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    Of course. But I'm still curious about references regarding this kind of safe set. – ConT Mar 24 '23 at 09:59
  • I am not aware of any reference regarding that kind of set. Not everything is defined and definitions are necessarily unique when it comes to research. There is not much context to your question as well. – KBS Mar 24 '23 at 12:18

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