**Controllability & Observability**

**1. A system is said to be_____________ if it is possible to transfer the system state from any initial state to any desired state in finite interval of time.**

a) Controllable

b) Observable

c) Cannot be determined

d) Controllable and observable

**Answer:** a

**Explanation:** By definition a system is said to be controllable, if it is possible to transfer the system state from any initial state to any desired state in finite interval of time.

**2. A system is said to be_________________ if every state can be completely identified by measurements of the outputs at the finite time interval.**

a) Controllable

b) Observable

c) Cannot be determined

d) Controllable and observable

**Answer:** b

**Explanation:** By definition, a system is said to be observable, if every state can be completely identified by measurements of the outputs at the finite time interval.

**3. Kalman’s test is for :**

a) Observability

b) Controllability

c) Optimality

d) Observability and controllability

**Answer:** d

**Explanation:** Kalman’s test is the test that is done for the controllability and observability by solving the matrix by kalman’s matrix individually for both tests.

**4. Consider a system if represented by state space equation and x1 (t) =x2 (t), then the system is:**

a) Controllable

b) Uncontrollable

c) Observable

d) Unstable

**Answer:** b

**Explanation:** After calculating the matrix which for controllable system and finding the determinant and should not be zero but in this case comes to be zero.

**5. For the system,**

** which of the following statements is true?**

a) The system is controllable but unstable

b) The system is uncontrollable and unstable

c) The system is controllable and stable

d) The system is uncontrollable and stable

**Answer:** b

**Explanation:** By Kalman’s stability test the system is uncontrollable and root of the characteristic equation lies on the right side of the s-plane.

**6. A transfer function of the system does not have pole-zero cancellation? Which of the following statements is true?**

a) System is neither controllable nor observable

b) System is completely controllable and observable

c) System is observable but uncontrollable

d) System is controllable and unobservable

**Answer:** b

**Explanation:** If the transfer function of the system does not have pole-zero cancellation then it is completely controllable and observable.

**7. Complex conjugate pair:**

a) Center

b) Focus point

c) Saddle point

d) Stable node

**Answer:** b

**Explanation:** Complex conjugate pair is the complex pair of the roots of the equation and has a focus point.

**8. Pure imaginary pair:**

a) Centre

b) Focus point

c) Saddle point

d) Stable node

**Answer:** a

**Explanation:** Pure imaginary pair is the nature of the root of the equation that has no real part only has the nature of center for linearized autonomous second order system.

**9. Real and equal but with opposite sign.**

a) Center

b) Focus point

c) Saddle point

d) Stable node

**Answer:** c

**Explanation:** Saddle point are real and equal with opposite sign and these points are called the saddle point as the points are different with real and equal with opposite sign.

**10. Real distinct and negative.**

a) Center

b) Focus point

c) Saddle point

d) Stable node

**Answer:** d

**Explanation:** Stable node is real distinct and negative and this node is stable as the points or roots are real and neative lying on the left side of the plane.

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