1. Consider the following properties attributed to state model of a system:

- State model is unique.
- Transfer function for the system is unique.
- State model can be derived from transfer function of the system.

Which of the above statements are correct?

- i, ii and iii
- i and ii only
- ii and iii only
- i and iii only

2. The state equations in the phase variable canonical form can be obtained from the transfer function by

- parallel decomposition
- inverse decomposition
- direct decomposition
- cascaded decomposition

3. When a transfer function model is converted into state-space model, the order of the system may be reduced during which one of the following conditions?

- The order of the system will never get changed.
- Pole, zero cancellation takes place.
- Some of the variables are hidden.
- Some of the variables are not considered.

4. Consider the following statements with respect to a system represented by its state-space model

$\dot x = Ax + Bu$ and Y = Cx

- The static vector x of the system is unique.
- The eigen values of A are the poles of the system transfer function.
- The minimum number of state variables required is equal to the number of independent energy storage elements in the system.

Which of these statements are correct?

- i and ii
- ii and iii
- i and iii
- i, ii and iii

5. The transfer function for the state variable representation

$\dot x = Ax + Bu$ and Y = Cx + Du, is given by

- C(sI – A)
^{-1}D + B - D(sI – A)
^{-1}B + C - B(sI – A)
^{-1}C + D - C(sI – A)
^{-1}B + D