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

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

Which of the above statements are correct?

1. i, ii and iii
2. i and ii only
3. ii and iii only
4. i and iii only

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

1. parallel decomposition
2. inverse decomposition
3. direct decomposition
4. 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?

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

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

and Y = Cx

1. The static vector x of the system is unique.
2. The eigen values of A are the poles of the system transfer function.
3. 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?

1. i and ii
2. ii and iii
3. i and iii
4. i, ii and iii

5. The transfer function for the state variable representation

and Y = Cx + Du, is given by

1. C(sI – A)^-1 D + B
2. D(sI – A)^-1 B + C
3. B(sI – A)^-1 C + D
4. C(sI – A)^-1 B + D