In [@singh1994], the authors build a robust minimal time control for spacecraft’s attitude maneuvers by canceling the poles of some transfer function. A remarkable fact is that the robustified control presents more switchings than the minimal time control. In this case, the robustness is evaluated as the maximum amplitude on a Bode diagram (see also [@liu1992] and [@liu1993] for similar works). In [@You2000], the authors observe that bang-bang controls are intrinsically not robust, and use pieces of singular trajectories (hence, not bang-bang) to overcome this issue.

In the $\mathcal{H}_2$ and $\mathcal{H}_{\infty}$ theories, control systems are often written in the frequency domain using the Laplace transform. For a transfer matrix $G(s)$, the two classical measures for performance are (see [@Doyle1989; @zhou1996robust]) the $\mathcal{H}_2$ norm and the $\mathcal{H}_{\infty}$ norm respectively: $$\left\|G\right\|_{2} = \left(\frac{1}{2 \pi} \int^{+ \infty}_{- \infty}{\text{Trace}(G(j \omega) G(j \omega)^*) d\omega} \right)^{1/2}\qquad\textrm{and}\qquad
\left\|G\right\|_{\infty} = \sup_{\omega \in {\mathbb{R}}} \overline{\sigma}(G(j \omega)),$$ where $\overline{\sigma}(G)$ is the largest singular value of $G$.

In the linear quadratic theory, the question of optimal tracking has been widely addressed: given a reference trajectory $\xi(\cdot)$, we track it with a solution of some control system $\dot{x}(t) =f(x(t),u(t))$, minimizing a cost of the form $$\int_0^{t_f} \left( \Vert x(t)-\xi(t)\Vert_W^2 + \Vert u(t)\Vert_U^2 