  We present a theoretical formalism for resonance fluorescence radiating from
a two-level system (TLS) driven by any periodic driving and coupled to multiple
reservoirs. The formalism is derived analytically based on the combination of
Floquet theory and Born-Markov master equation. The formalism allows us to
calculate the spectrum when the Floquet states and quasienergies are
analytically or numerically solved for simple or complicated driving fields. We
can systematically explore the spectral features by implementing the present
formalism. To exemplify this theory, we apply the unified formalism to
comprehensively study a generic model that a harmonically driven TLS is
simultaneously coupled to a radiative reservoir and a dephasing reservoir. We
demonstrate that the significant features of the fluorescence spectra, the
driving-induced asymmetry and the dephasing-induced asymmetry, can be
attributed to the violation of detailed balance condition, and explained in
terms of the driving-related transition quantities between Floquet-states and
their steady populations. In addition, we find the distinguished features of
the fluorescence spectra under the biharmonic and multiharmonic driving fields
in contrast with that of the harmonic driving case. In the case of the
biharmonic driving, we find that the spectra is significantly different from
the result of the rotating-wave approximation (RWA) under the multiple
resonance conditions. By the three concrete applications, we illustrate that
the present formalism provides a routine tool for comprehensively exploring the
fluorescence spectrum of periodically strongly driven TLSs.
