  Dynamical kicking systems possess rich topological structures. In this work,
we study Floquet states of matter in a non-Hermitian extension of double kicked
rotor model. Under the on-resonance condition, we find various non-Hermitian
Floquet topological phases, with each being characterized by a pair of
topological winding numbers. A generalized mean chiral displacement is
introduced to detect these winding numbers dynamically in two symmetric time
frames. Furthermore, by mapping the system to a periodically quenched lattice
model, we obtain the topological edge states and unravel the bulk-edge
correspondence of the non-Hermitian double kicked rotor. These results uncover
the richness of Floquet topological states in non-Hermitian dynamical kicking
systems.
