would like to acknowledge Prof. Jian Li for providing an implementation of examples from [@08:Guo].

\[sec:appendix\]

Proof of Theorem \[theo:robustSDP\] {#app A}
-----------------------------------

We start the proof by first stating the $\mathcal{S}$-Procedure lemma which helps us to turn the optimization problem with infinitely many quadratic constraints into a convex problem with finite number of LMIs.

\[lem 6\]($\mathcal{S}$-Procedure [@Beck2009a Lemma 4.1]): Let $f_k(\x): \mathbb{C}^n \rightarrow \mathbb{R}$, $k = 0,1$, be defined as $f_k(\x) = \x^H\mathbf{A}_k \x
+ 2 \textrm{Re} \{\mathbf{b}_k^H \x \} + c_k$, where $\mathbf{A}_k = \mathbf{A}_k^H \in \mathbb{C}^{n
\times n}, \mathbf{b}_k \in \mathbb{C}^n$, and $c_k \in
\mathbb{R}$. Then, the statement (implication) $f_0(\x) \geq 0$ for all $\x \in \mathbb{C}^n$ such that $f_1(\x) \geq 0$ holds if and only if there exists $\beta \geq 0$ such that[^2] $$\left[ \begin{array}{cc}
\mathbf{A}_0 & \mathbf{b}_0 \\
\mathbf{b}_0^H & c_0
\end{array}\right] - \beta \left[ \begin{array}{cc}
\mathbf{A}_1 & \mathbf{b}_1 \\
\mathbf{b}_1^H & c_1
\end{array}\right] \succeq 0,$$ if there exists a point $\mathbf{\hat{x}}$ with $f_1(\mathbf{\hat{x}}) > 0$.

The constraints in the optimization problem can be rewritten as the following functions of $\atil(\r)$ for $\r \in \Omega_S$ and $\r \in \Omega_T$. For notation simplicity we only specify the set from which the control points are drawn, and 