A Commentary, Critical, Practical, and Explanatory on the Old and New Testaments, by Robert Jamieson, A.R. Fausset and David Brown  at sacred-texts.com
psa 113:1God's majesty contrasted with His condescension and gracious dealings towards the humble furnish matter and a call for praise. The Jews, it is said, used this and Psalms 114-118 on their great festivals, and called them the Greater Hallel, or Hymn. (Psa 113:1-9)
Earnestness and zeal are denoted by the emphatic repetitions.
servants of the Lord--or, all the people of God.
name of the Lord--perfections (Psa 5:11; Psa 111:9).
psa 113:3From the rising, &c.--all the world.
psa 113:4God's exaltation enhances His condescension;
psa 113:7which condescension is illustrated as often in raising the worthy poor and needy to honor (compare Sa1 2:8; Psa 44:25).
psa 113:9On this special case, compare Sa1 2:21. Barrenness was regarded as a disgrace, and is a type of a deserted Church (Isa 54:1).
the barren woman . . . house--literally, "the barren of the house," so that the supplied words may be omitted.