This paper addresses the design of a controller family that, given a continuous-time linear plant sampled at a varying rate, asymptotically stabilizes the closed loop. Under the assumption of having a finite and known set of allowable sampling intervals, the problem is formulated as that of stabilizing a discrete-time switched system (DTSS). The solution approach consists in choosing the controller parameters in order for the Lie algebra generated by the closed-loop DTSS-matrices to be solvable, as this property guarantees the existence of a common Lyapunov function for the control system. The results can be applied to design digital controllers sharing resources, as it is the case of networked control systems, where the need of adapting the rate of task scheduling may originate significant sampling time variations.