For the system in Part 1, consider the state variables v 1 (t) = y(t) v 2 (t)=y(t) + y(t) x(t) (a) Obtain the matrix A 2 and the vectors b 2 and c T 2 for the state and the output equations that realize the ordinary differential equation in Part 1. (b) Draw a block diagram for the state variables and output realization. (c) How do A 2 , b 2 , and c T 2 obtained above compare with the ones in Part 1? (d) In the block diagram in Part 1, change the summers into nodes, and the nodes into summers, invert the direction of all the arrows, and interchange x(t) and y(t), i.e., make the input and output of the previous diagram into the output and the input of the diagram in this part. This is the dual of the block diagram in Part 1. How does it compare to your block diagram obtained in item (b)? How do you explain the duality?

Question: For the system in Part 1, consider the state variables v 1 (t) = y(t) v 2 (t)=y(t) + y(t) x(t) (a) Obtain the

For the system in Part 1, consider the state variables

v₁(t) = y(t) v₂(t)=ẏ(t) + y(t) − x(t)

(a) Obtain the matrix A₂ and the vectors b₂ and c^T₂ for the state and the output equations that realize the ordinary differential equation in Part 1.

(b) Draw a block diagram for the state variables and output realization.

(d) In the block diagram in Part 1, change the summers into nodes, and the nodes into summers, invert the direction of all the arrows, and interchange x(t) and y(t), i.e., make the input and output of the previous diagram into the output and the input of the diagram in this part. This is the dual of the block diagram in Part 1. How does it compare to your block diagram obtained in item (b)? How do you explain the duality?

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