Question: 1. (25 points) Consider the controlled linear system in R3: dy = dt Ay + Bu on (0,T) Yo, (1) y(0) - where 1 1

1. (25 points) Consider the controlled linear system in R3: dy

1. (25 points) Consider the controlled linear system in R3: dy = dt Ay + Bu on (0,T) Yo, (1) y(0) - where 1 1 2 0 A= and B= 0 0 2 1 0 0 2 1 Compute the associated Gramian matrix for any T > 0. (b) Is the system (1) controllable at any positive time T? (Justify your answer!) 1. (25 points) Consider the controlled linear system in R3: dy = dt Ay + Bu on (0,T) Yo, (1) y(0) - where 1 1 2 0 A= and B= 0 0 2 1 0 0 2 1 Compute the associated Gramian matrix for any T > 0. (b) Is the system (1) controllable at any positive time T? (Justify your answer!)

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