Nonequilibrium steady states (NESSs) in periodically driven
dissipative quantum systems are vital in Floquet engineering. We develop
a general theory for high-frequency drives with Lindblad-type
dissipation to characterize and analyze NESSs. This theory is based on
the high-frequency (HF) expansion with linear algebraic numerics and
without numerically solving the time evolution. Using this theory, we
show that NESSs can deviate from the Floquet-Gibbs state depending on
the dissipation type. We also show the validity and usefulness of the
HF-expansion approach in concrete models for a diamond nitrogen-vacancy
(NV) center, a kicked open XY spin chain with topological phase
transition under boundary dissipation, and the Heisenberg spin chain in
a circularly-polarized magnetic field under bulk dissipation. In
particular, for the isotropic Heisenberg chain, we propose the
dissipation-assisted terahertz (THz) inverse Faraday effect in quantum
magnets. Our theoretical framework applies to various time-periodic
Lindblad equations that are currently under active research.