\mathcal{E}_{\r}$. The perturbation vectors $\atil(\r)$ are unknown but deterministically bounded. In the following we illustrate the worst-case performance, i.e., using the worst steering vectors to calculate the power distribution at each point. We start by illustrating the beampattern for the non-robust covariance matrix $\R_{nr}$ under the worst steering vectors. Fig. \[fig:NonRobustWorst\] shows how steering vector errors can degrade the array performance. Notice that in the worst-case, there is a substantial power leakage that occurs in the healthy tissue surrounding the tumor compared to Fig. \[fig:nominal\]. While, in Fig. \[fig:RobustWorst\], the robust optimal covariance matrix $\R^\star$, i.e., the solution to , is used to calculate the power for the worst steering vectors. Comparing Fig. \[fig:NonRobustWorst\] and Fig. \[fig:RobustWorst\], we see that by taking model uncertainties into account it is possible to obtain a noticeable increase in power in the tumor region for the worst case, and importantly, dramatic reductions of power deposited in the healthy tissue.

![Power distribution (transmit beampattern in dB) for the perturbed scenario, i.e., using $\R_{nr}$ and $\atil(\r) \in \mathcal{E}_{\r}$.[]{data-label="fig:NonRobustWorst"}](worst_nr_05_07lines "fig:"){width="\columnwidth" height="5.5cm"}\

![Power distribution (transmit beampattern in dB) for the perturbed scenario, i.e., using $\R^\star$ and $\atil(\r) \in \mathcal{E}_{\r}$.[]{data-label="fig:RobustWorst"}](worst_r_05_07lines "fig:"){width="\columnwidth" height="5.5cm"}\

To finalize the numerical analysis, we provide 