Q2 (16) RLD/Backstepping A pendulum with moving suspension point is de- cribed by, mL + mgsin(0) + kL = T/L+ mh(t)cos(0) where, = h(t) horizontal acceleration of the suspension point; T = torque applied at the suspension point; m = pendulum mass; L = pendulum length; k friction coefficient; = (t) angle from the vertical. The aim is to stabilize the pendulum at 0 = 0. (a) Assuming h(t) is measured and thus known de- sign a RLD based control and prove closed loop stability. (b) Now suppose it is only known that |h(t)| 1. Show how to modify the RLD control to still achieve closed loop stability.