Judah was his sanctuary - His home; his abode; his sacred dwelling-place. Judah was the principal or leading tribe, recognized as the tribe where power was to be concentrated, and from which the Messiah was to proceed Genesis 49:8-12; and hence, the name was early used to denote the entire people, and ultimately, as modified in the word Jews, became the common name of the nation.
And Israel his dominion - The nation that he ruled; the nation that had his law; the nation that he governed by his presence - or, of which he was the recognized king. There can be no doubt that the reference here is to God, but it is remarkable that the name “God” is not used. Perhaps the reason may be that this psalm was designed to be employed in connection with the preceding one, and as that consists entirely of the praises of God, it was not necessary to repeat the name when his praise was to be continued under another form, and in connection with another line of thought.