## Description

1. Consider the nonlinear system:

x˙ 1 = x2

x˙ 2 = cos(x3) + x1 + u

x˙ 3 = x4

x˙ 4 = x1 + u

y = x1

Find the relative degree of the system and convert it to the normal form. Design a feedback

linearization control law for this system. Is the system stable? Plot relevant phase portraits/state

trajectories to justify your answer.

2. Design a sliding-mode controller for the system given below, to track xd(t) = sin(t)

x¨ + a(t) ˙x

2

cos(5x) = b(t)u

Where 1 ≤ a(t) ≤ 2 and 4 ≤ b(t) ≤ 8. Introduce a boundary layer to remove chattering. Plot s(t),

x˙(t) vs x(t) and u(t).