General:
* Confinement
* Imprisonment
* Detention
* Enclosed
* Bound
* Restraint
* Bondage
For animals:
* Enclosure
* Zoo
* Cage
* Pen
* Aviary
Figurative:
* Subjugation
* Enslavement
* Oppression
* Control
The best synonym to use will depend on the specific meaning you want to convey.