  This paper considers the stabilization of unknown switched linear systems
using data. Instead of a full system model, we have access to a finite number
of trajectories of each of the different modes prior to the online operation of
the system. On the basis of informative enough measurements, formally
characterized in terms of linear matrix inequalities, we design an online
switched controller that alternates between a mode detection phase and a
stabilization phase. Since the specific currently-active mode is unknown, the
controller employs the most recent online measurements to determine it by
implementing computationally efficient tests that check compatibility with the
set of systems consistent with the pre-collected measurements. The
stabilization phase applies the stabilizing feedback gain corresponding to the
identified active mode and monitors the evolution of the associated Lyapunov
function to detect switches. When a switch is detected, the controller returns
to the mode-detection phase. Under average dwell- and activation-time
assumptions on the switching signal, we show that the proposed controller
guarantees a practical stability property of the closed-loop switched system.
Various simulations illustrate our results.
