  Search for stable high-pressure compounds in the Ti--H system reveals the
existence of titanium hydrides with new stoichiometries, including
Ibam-Ti$_2$H$_5$, I4/m-Ti$_5$H$_{13}$, I$\bar{4}$-Ti$_5$H$_{14}$, Fddd-TiH$_4$,
Immm-Ti$_2$H$_{13}$, P$\bar{1}$-TiH$_{12}$, and C2/m-TiH$_{22}$. Our
calculations predict I4/mmm $\rightarrow$ R$\bar{3}$m and I4/mmm $\rightarrow$
Cmma transitions in TiH and TiH$_2$, respectively. Phonons and the
electron--phonon coupling of all searched titanium hydrides are analyzed at
high pressure. It is found that Immm-Ti$_2$H$_{13}$ rather than the highest
hydrogen content C2/m-TiH$_{22}$, exhibits the highest superconducting critical
temperature T$_{c}$. The estimated T$_{c}$ of Immm-Ti$_2$H$_{13}$ and
C2/m-TiH$_{22}$ are respectively 127.4--149.4 K ($\mu^{*}$=0.1-0.15) at 350 GPa
and 91.3--110.2 K at 250 GPa by numerically solving the Eliashberg equations.
One of the effects of pressure on T$_{c}$ can be attributed to the softening
and hardening of phonons with increasing pressure.
