  In the composite Higgs models, originally proposed by Georgi and Kaplan, the
Higgs boson is a pseudo Nambu-Goldstone boson (pNGB) of spontaneous breaking of
a global symmetry. In the minimal version of such models, global SO(5) symmetry
is spontaneously broken to SO(4), and the pNGBs form an isospin doublet field,
which corresponds to the Higgs doublet in the Standard Model (SM). Predicted
coupling constants of the Higgs boson can in general deviate from the SM
predictions, depending on the compositeness parameter. The deviation pattern is
determined also by the detail of the matter sector. We comprehensively study
how the model can be tested via measuring single and double production
processes of the Higgs boson at LHC and future electron-positron colliders. The
possibility to distinguish the matter sector among the minimal composite Higgs
models is also discussed. In addition, we point out differences in the cross
section of double Higgs boson production from the prediction in other new
physics models.
