Use - synthesis to design a controller for the acc

Question

Problem -

Use  μ - synthesis to design a controller for the ACC benchmark problem that satisfies the following performance specifications:

(i) closed loop system stable for all k ∈ [0.5, 2],

(ii) for the value of k = 1.25, the control action and the displacement of the second mass in response to an impulse input acting on m₂ satisfies: |u(u)| ≤ 1 and settling time T_y2 ≤ 15 sec.

Hint: If you are using a bilinear transformation, try p₁ small (≤ 0.15) and p₂ large (2000).