**2003**

1. The zero input response of a system given by the state space equation

**Solution :**

**https://www.youtube.com/watch?v=BzTXlRJ5M9k**

**2004**

2. The state variable equations of a system are:

ẋ

_{1}= -3x

_{1}-x

_{2}+ u

ẋ

_{2}= 2x

_{1}

y = x

_{1}+ u

Then the system is

a) controllable but not observable

b) observable but not controllable

c) neither controllable nor observable

d) controllable and observable

**Solution :**https://www.youtube.com/watch?v=CVH0VsecVuQ

3. The state transition matrix e

^{At}for the given matrix A, is

**Solution :**https://www.youtube.com/watch?v=w9zVGFsZ3Bw

**2005**

4. A linear system is equivalently represented by two sets of state equations

Ẋ = AX + BU and Ẇ = CW + DU.

The eigen values of the representations are also computed as |λ| and |μ|. Which one of the following statements is TRUE?

**Answer :**

**Solution :**

**2006**

5. A linear system is described by the following state equation, then the state transition matrix of the system is

**Solution :**https://www.youtube.com/watch?v=SdKm17kCbFg

**2007**

6. The state space representation of a separately excited DC servo motor dynamics is given as

where ω is the speed of the motor, i

_{a}is the armature current and u is the armature voltage. The transfer function of the motor is

**Solution :**https://www.youtube.com/watch?v=jTt-sWQZS0Y

**Statement for Linked Answer Questions 7 & 8:**

7. The eigen value and eigen vector pairs (λ

_{i}, v

_{i}) for the system are

**Solution :**

8. The system matrix A is

**Solution :**

**2008**

9. A signal flow graph of a system is given below.

The set of equations that correspond to this signal flow graph is

**Solution :**https://www.youtube.com/watch?v=cxlX8Rpj9cs

**2009**

10. consider the system,

where p and q are arbitrary real numbers, which one of the following statements about the controllability of the system is TRUE?

a) the system is completely state controllable for any non zero values of p and q

b) only p=0 and q=0 result in controllability

c) the system is uncontrollable for all values of p and q

d) we cannot conclude about controllability from the given data

**Solution :**https://www.youtube.com/watch?v=MvBkDRPjIcY

**2010**

**Common Data Questions:(11 and 12)**

The signal flow graph of a system is shown below.

11. The state variable representation of the system can be

**Solution :**https://www.youtube.com/watch?v=-4PqIhkiPD0

12. The transfer function of the system is

**Solution :**https://www.youtube.com/watch?v=kT5TsnSEl9g

**2011**

13. The block diagram of a system with one input u and two outputs y

_{1}and y

_{2}is given below.

A state space model of the system in terms of the state vector ẋ and the vector ẏ = [y

_{1}y

_{2}]

^{T}is

**Solution :**https://www.youtube.com/watch?v=CsciojvPQF8

**2012**

14. The state variable description of an LTI system is by

where y is the output and u is the input. The system is controllable for

a) a

_{1}≠ 0, a

_{2}= 0, a

_{3}= 0

b) a

_{1}= 0, a

_{2}≠ 0, a

_{3}≠ 0

c) a

_{1}= 0, a

_{2}≠ 0, a

_{3}= 0

d) a

_{1}≠ 0, a

_{2}≠ 0, a

_{3}= 0

**Solution :**https://www.youtube.com/watch?v=dPCv96oD6Ow

**2013**

15. The signal flow graph for a system is given below.

The transfer function Y(s)/U(s) for this system is

**Solution :**https://www.youtube.com/watch?v=ndeVYkf7j6w

16. The state diagram of the system is shown below. A system is described by the state variable equations

a. State variable equations of the system shown in the above figure is

b. The state transition matrix e

^{At}of the system shown in the figure above is

**Solution (a & b) :**https://www.youtube.com/watch?v=wnfqGfnPFcs

**2014**

17. A system is described by the following differential equation, where u(t) is the input to the system and y(t) is the output of the system.

When y(0) = 1 and u(t) is a unit step function, y(t) is

**Solution :**https://www.youtube.com/watch?v=6tsdXBAfClY

18. consider the state space model of a system, as given below.

The given system is

a) controllable and observable

b) uncontrollable and observable

c) uncontrollable and unobservable

d) controllable and unobservable

**Solution :**https://www.youtube.com/watch?v=MqFMHFSyGgk

19. An unforced linear time invariant (LTI) system is represented by

If the initial conditions are x1(0) = 1 and x2(0) = - 1, then the solution of the state equation is

**Solution :**https://www.youtube.com/watch?v=PW4_N3VeGPs

20. Consider the state space system expressed by the signal flow diagram shown in the figure.

The corresponding system is

a) always controllable

b) always observable

c) always stable

d) always unstable

**Solution :**https://www.youtube.com/watch?v=kx74sDKotOs

21. The state equation of a second order linear system is given by

**Solution :**https://www.youtube.com/watch?v=2Yx8ux4wY4U

22. The state transition matrix Φ(t) of a system,

**Solution :**https://www.youtube.com/watch?v=tTLuvoMF_Jc

**2015**

23. The state variable representation of a system is given as

The response y(t) is

a) sin (t)

b) 1 – e

^{t}

c) 1 – cos (t)

d) 0

**Solution :**https://www.youtube.com/watch?v=Ax6VxSUUJtA

24. A network is described by the state model as

then the transfer function H(s) = (Y(s)/U(s)) is

**Solution :**https://www.youtube.com/watch?v=z5t9oMUeA-U