  Second-order topological insulators (SOTI) exhibit protected gapless boundary
states at their hinges or corners. In this paper, we propose a generic means to
construct SOTIs in static and Floquet systems by coupling one-dimensional
topological insulator wires along a second dimension through dimerized hopping
amplitudes. The Hamiltonian of such SOTIs admits a Kronecker sum structure,
making it possible for obtaining its features by analyzing two constituent
one-dimensional lattice Hamiltonians defined separately in two orthogonal
dimensions. The resulting topological corner states do not rely on any delicate
spatial symmetries, but are solely protected by the chiral symmetry of the
system. We further utilize our idea to construct Floquet SOTIs, whose number of
topological corner states is arbitrarily tunable via changing the hopping
amplitudes of the system. Finally, we propose to detect the topological
invariants of static and Floquet SOTIs constructed following our approach in
experiments by measuring the mean chiral displacements of wavepackets.
