Using "the undersigned" is kind of legal jargon. Legal documentation is its own weird area, and I would argue that it's chock full of style that is pretty awful. If there's some legal reason you can't just use "I" as the subject of both sentences, it would be stylistically better to combine the ideas into one sentence. "The undersigned respectfully moves to adjourn today's meeting because the committee can make no progress until all resource speakers are present."
If you start the first sentence with "I, the undersigned, respectfully . . ." then you can legitimately start the second sentence with just "I." The trick here is that you want to ensure your readers understand that the subject of both sentences is the same person.
But if you can leave out "the undersigned" altogether, do it!