  We consider the data-driven stabilization of discrete-time linear
time-varying systems. The controller is defined as a linear state-feedback law
whose gain is adapted to the plant changes through a data-based
event-triggering rule. To do so, we monitor the evolution of a data-based
Lyapunov function along the solution. When this Lyapunov function does not
satisfy a designed desirable condition, an episode is triggered to update the
controller gain and the corresponding Lyapunov function using the last
collected data. The resulting closed-loop dynamics hence exhibits both physical
jumps, due to the system dynamics, and episodic jumps, which naturally leads to
a hybrid discrete-time system. We leverage the inherent robustness of the
controller and provide general conditions under which various stability notions
can be established for the system. Two notable cases where these conditions are
satisfied are treated, and numerical results illustrating the relevance of the
approach are discussed.
