Feedback stabilization via dynamic fixed gain controls: Preliminary report

We synthesize scanning feedback controls {??i(t)} for the vibrating string equation ytt(x,t) = yxx(x,t) + Ry(x,t) +??i=1 N ??(x-??i(t))y(x,t), 0 < x < 1, y = 0 at x = 0,1. so that (y,yt) ?? (0,0) at t ?? ?? in the weak topology of H0 1(0, 1) ?? L2(0, 1).