The key term for praise in Psalm 113 is halal. Halal is a very special word for excited boasting. Most particularly, excited boasting in the living Yahweh.
[Ronald B. Allen, And I Will Praise Him, 114]
"The word 'Hallelujah' is a Hebrew word that is a compound term. It is made of the plural imperative of the verb 'to praise' coupled to the short form of the name of God, 'Yah' (or 'Jah')."
[Ronald B. Allen, And I Will Praise Him, 113]