Even though I do not think these were written by the same person or even in the same time period it is interesting that Psalm 135 and 136 have similar elements. Please image David in 1 Chronicles 15:11 instructing his Praise Team to sing Psalm 135 as they carry the Ark to Jerusalem. Then image Ezra in Chapter 3:11 separating the congregation into halves and having one group singing the first part of each verse while the other group responds with “His love endures forever.”
These Psalms are included in the section of the “songs of ascents” which were traditionally sung as people went up to the Temple in Jerusalem. Psalm 115 and 118 share the idea of verse 19 and 20 of Psalm 135; the house of Israel, Aaron, Levi and those who fear Him. Psalm 135:4 talks about Jacob and Israel giving each a different emphasis. They also have a historical component remembering God’s great deliverance form Egypt and the defeat of Og and Sihon which marked the beginning of the conquest of the Promised Land. The blue sections highlight His control over nature and thus being in charge of their daily lives.
Thanks to BibleGateway.com they are a great resource.