3.6 Consider the system with bounded control U₁ and ---- 1 0 B If the initial point is x° = (r cos a, r sin x)T, show that x = (₁, 0) if a bounded control u, exists such that T COS α = -*u, (t)sin t dt, r sin α = - Ső u₁(T)cos T dt. Deduce that, if t₁ = π and a is kept fixed, all points of the line -2 ≤r≤ 2 are in (7, 0). Hence show that (x, 0) is the closed disc |x ≤2 Find (nz, 0) and show that 6(0) = 2. (This exercise gives a direct proof of complete controllability for a system in which the eigenvalues of A have zero real parts. See §3.3(4).)

3.6 Consider the system with bounded control U₁ and ---- 1 0 B If the initial point is x° = (r cos a, r sin x)T, show that x = (₁, 0) if a bounded control u, exists such that T COS α = -*u, (t)sin t dt, r sin α = - Ső u₁(T)cos T dt. Deduce that, if t₁ = π and a is kept fixed, all points of the line -2 ≤r≤ 2 are in (7, 0). Hence show that (x, 0) is the closed disc |x ≤2 Find (nz, 0) and show that 6(0) = 2. (This exercise gives a direct proof of complete controllability for a system in which the eigenvalues of A have zero real parts. See §3.3(4).)