  We study quantum Floquet (periodically-driven) systems having continuous
dynamical symmetry (CDS) consisting of a time translation and a unitary
transformation on the Hilbert space. Unlike the discrete ones, the CDS strongly
constrains the possible Hamiltonians $H(t)$ and allows us to obtain all the
Floquet states by solving a finite-dimensional eigenvalue problem. Besides,
Noether's theorem leads to a time-dependent conservation charge, whose
expectation value is time-independent throughout evolution. We exemplify these
consequences of CDS in the seminal Rabi model, an effective model of a
nitrogen-vacancy center in diamonds without strain terms, and Heisenberg spin
models in rotating fields. Our results provide a systematic way of solving for
Floquet states and explain how they avoid hybridization in quasienergy
diagrams.
