Controllable Combat Pets are pets that are either controllable inherently (Tyrannon's Familiar, Wolves from "Command Animals", etc.) or pets that can be controlled through an upgrade (Upgrading Ritual Summons with "Meek Inheritance" allows them to be controlled).
Controlled Combat Pets are generally permanent until either killed or dismissed.
Damage scales with Intelligence
Health scales with Presence
If you have more than one controllable pet out, they all share the same pet command bar