The dragonborn is able to absorb dragon souls of each dragon that he slays. Alduin is capable of resurrecting dead dragons to be his servants. Now is it possible that the dragonborn can have similar power? The ancient nords invented a dragon shout (Dragonrend) to force the dragon to land. Now is it possible to invent a whole new shout (and not just read on some wall) to resurrect dragons by giving them a dragon soul?

You would have to do more than give them a soul, you would have to know how to restore their bodies. Alduin's resurrection "magic" is actually recreating their physical form from whatever was left of their remains, giving their souls a new fully functioning body.

You'd have to do two things - recreate their physical bodies, and then put souls back into them. And at any rate I think when the Dragonborn absorbs a dragon's soul the individual dragon's soul is obliterated or subsumed into the Dragonborn's soul, and/or is translated into the raw power and knowledge that accumulates within the Dragonborn. It doesn't just sit there as an individual soul that the Dragonborn can whip out and put back again.