Those short bars are part of the sway bar. It connects to the upper control arm, goes back about a foot, turns inside the fender, runs along the firewall and comes out at the other fender, etc.
That your car has the sway bar attached at both control arms is a positive sign. I've heard of sway bars disconnecting from the control arm. I suppose it's possible that yours is broken in the middle, but that would make all sorts of noise. Maybe it's time to check the sway bar bushings. There are bushings in each control arm and at least 2 along the firewall.
Is your front left shock absorber properly attached on top?