- We use the notation \(a \triangleq b\) to denote that \(a\) is equal to \(b\) by definition.
- We denote by \(\Re\) the set of real numbers, by \(\mathbb Z\) the set of integers and by \(\mathbb N \triangleq \{0, \, 1, \, \ldots \}\) the set of natural numbers. The set \(\mathbb N_+\) is defined as \(\mathbb N_+ \triangleq \{1, \, 2, \, \ldots \}\).
- \(f(\cdot)\) denotes a function where \((\cdot)\) stands for the undesignated variables. \(f(x)\) denotes the value of \(f(\cdot)\) at the point \(x\). \(f\colon A \rightarrow B\) indicates that the domain of \(f(\cdot)\) is in the space \(A\) and its range in the space \(B\).
- We say that a function \(f \colon \Re^n \to \Re\) is once continuously differentiable if \(f(\cdot)\) is defined on \(\Re^n\), and if \(f(\cdot)\) has a continuous derivative on \(\Re^n\).
- For \(f \colon \Re \to \Re\), we denote by \(f^{(N)}(\cdot)\) its \(N\)-th derivative.
- For \(f \colon \Re \to \Re\) and \(t \in \Re\), we denote by \(f(t^-) \triangleq \lim_{s \uparrow t} f(s)\) the limit from below.
- For \(s \in \Re\), we define the ceiling function as \(\lceil s \rceil \triangleq \arg \min\{ k \in \mathbb Z \ | \ s \le k \}\).
- For \(t_R \in \Re\) and \(t_I \in \mathbb N\), we write \(t^+ \triangleq (t_R, \, t_I)^+\) for the right limit at \(t\). It holds that \((t_R, \, t_I)^+ \Leftrightarrow (\lim_{\epsilon \to 0} (t_R+\epsilon), t_{I_{max}})\), where \(I_{max}\) is the largest occurring integer of superdense time. Similarly, we write \(\mathbin{^-t}\) for the left limit at \(t\), for which it holds that \(\mathbin{^-(t_R, \, t_I)} \Leftrightarrow (\lim_{\epsilon \to 0} (t_R-\epsilon), 0)\).
- We write a requirement
*shall*be met if it must be fulfilled. If the feature that implements a shall requirement is not in the final system, then the system does not meet this requirement. We write a requirment*should*be met if it is not critical to the system working, but is still desirable.

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