Assignment 3

Due: Friday, 10 June at 10:00 (submit at the start of class)

  1. Given the following system:NE2_2a_top

    (a) Give the transformation matrix that would yield a new state vector with x1 and x2 swapped.

    (b) Determine the A and B matrices for the transformed system from (a).

    (c) Give the transformation matrix needed to define new variables z1 = x1 + x2 and z2 = 4 x2.

  2. Assess the controllability of the following systems:
    NE3_1cde 
  3. a) Show that the following system is not observable:

    b) Show that by modifying the output equation as follows, the system becomes observable:A3_q5_b
    You can use Matlab to calculate the rank of the controllability matrix for this part.