Let's begin with the first verse you quoted from in
Isaiah 11:
"There shall come forth a shoot from the stump of Jesse, and a branch from his roots shall bear fruit."
It is significant to notice the language used here. If David's house is compared to a stump that is felled, which in the previous chapter describes God's wrath, then this must mean that this passage refers to a time when all of the splendor and glory of David's house will be brought so low that it will appear near to the point of extinction. Interestingly, on this account he does not call it David, but Jesse; because the rank of that family had sunk so low, that it no longer appeared to be a royal family, but that of a mean peasant, such as the family of Jesse was, when David was unexpectedly called to the government of the kingdom. However, the
one promised to restore the kingdom is compared to a shoot and branch coming forth from such a poor condition and state.