  We consider the design of state feedback control laws for both the switching
signal and the continuous input of an unknown switched linear system, given
past noisy input-state trajectories measurements. Based on Lyapunov-Metzler
inequalities, we derive data-dependent bilinear programs whose solution
directly returns a provably stabilizing controller and ensures $\mathcal{H}_2$
or $\mathcal{H}_{\infty}$ performance. We further present relaxations that
considerably reduce the computational cost, still without requiring
stabilizability of any of the switching modes. Finally, we showcase the
flexibility of our approach on the constrained stabilization problem for a
perturbed linear system.
