  We use the quasienergy structure that emerges when a fluxonium
superconducting circuit is driven periodically to encode quantum information
with dynamically induced flux-insensitive sweet spots. The framework of Floquet
theory provides an intuitive description of these high-coherence working points
located away from the half-flux symmetry point of the undriven qubit. This
approach offers flexibility in choosing the flux bias point and the energy of
the logical qubit states as shown in [\textit{Huang et al., 2020}]. We
characterize the response of the system to noise in the modulation amplitude
and DC flux bias, and experimentally demonstrate an optimal working point which
is simultaneously insensitive against fluctuations in both. We observe a
40-fold enhancement of the qubit coherence times measured with Ramsey-type
interferometry at the dynamical sweet spot compared with static operation at
the same bias point.
