It doesn't matter if your model is Kanban, Agile, Waterfall, or RUP. You can't close out a project or task without first identifying the Acceptance Criteria. Acceptance criteria begins to take shape during the first moments of a project or task. If you are utilizing Kanban or Agile, everything pertaining to your deliverable should be captured on your story cards. This includes story details and acceptance (testing) criteria. Satisfying all acceptance criteria implies the needs of the customer have been met.
If you following Waterfall, RUP, or similar model, you would expect to identify acceptance criteria, along with scope description and project deliverables, in the project scope statement. (These are each components of a scope baseline)
It all goes back to requirements and stakeholders' satisfaction. Remember each requirement should add business value by linking to a business or project objective(s).
Those criteria, including performance requirements and essential conditions, must be met before project deliverables are accepted. Regardless of your model, spare yourself a lot of wasted time AND money by documenting acceptance criteria early.