State-Space Representation — MCQs – EE

1. The state-space representation of a system is based on:
(A) Differential equations
(B) Transfer function
(C) State variables and matrices
(D) Frequency response

2. The state vector in a state-space model contains:
(A) Only inputs
(B) Only outputs
(C) A minimal set of system variables describing the system
(D) Frequency components

3. The general form of a state-space model consists of:
(A) State and output equations
(B) Only input equations
(C) Only transfer functions
(D) Frequency-domain plots

4. In the state equation
(A) represents:
(A) Input gain
(B) System dynamics
(C) Output feedback
(D) Control input

5. In the output equation
(D) represents:
(A) Direct transmission from input to output
(B) System damping
(C) State dynamics
(D) Feedback path

6. The number of state variables in a system is equal to the number of:
(A) Inputs
(B) Energy storage elements
(C) Outputs
(D) Poles minus zeros

7. State-space analysis can be applied to:
(A) Only linear time-invariant systems
(B) Both linear and nonlinear systems
(C) Only discrete-time systems
(D) Only first-order systems

8. In a continuous-time state-space system, the derivative of the state vector depends on:
(A) Present input and previous outputs
(B) Present states and inputs
(C) Past inputs only
(D) Future values of the system

9. In the equation
(A) System response to initial conditions
(B) System response to input
(C) Feedback term
(D) Output error

10. The output equation
(A) How input affects state
(B) How state affects output
(C) How system poles are placed
(D) How error is minimized

11. The state-transition matrix Φ(t) is used to determine:
(A) System frequency
(B) The evolution of the state vector over time
(C) Input magnitude
(D) Stability margin

12. The eigenvalues of the A matrix are equal to:
(A) Zeros of the system
(B) Poles of the system
(C) State variables
(D) Gain constants

13. A system is completely controllable if:
(A) The controllability matrix has full rank
(B) The observability matrix has full rank
(C) The A matrix is diagonal
(D) The B matrix is zero

14. A system is completely observable if:
(A) The C matrix is zero
(B) The controllability matrix has full rank
(C) The observability matrix has full rank
(D) The A matrix has repeated roots

15. The state-space representation is particularly useful for:
(A) Single-input single-output systems only
(B) Multiple-input multiple-output systems
(C) Frequency response analysis
(D) Steady-state error analysis only

16. The Kalman canonical form is related to:
(A) Root-locus design
(B) Controllability and observability
(C) Steady-state response
(D) Frequency analysis

17. The system order in state-space representation equals the number of:
(A) Poles
(B) Zeros
(C) Feedback loops
(D) Outputs

18. The A matrix in a state-space model determines:
(A) System poles
(B) System zeros
(C) System gain
(D) Input scaling

19. The C matrix in a state-space model determines:
(A) System controllability
(B) How states affect the output
(C) How inputs affect states
(D) System zeros only

20. The state-space approach is superior to classical methods because it:
(A) Works only in frequency domain
(B) Can handle nonlinear and MIMO systems
(C) Avoids matrix algebra
(D) Uses only transfer functions

21. The dual of a controllable system is:
(A) Stable system
(B) Observable system
(C) Uncontrollable system
(D) Time-varying system

22. State feedback control is designed to:
(A) Change the system poles to desired locations
(B) Increase steady-state error
(C) Decrease damping
(D) Add zeros to the system

23. The observer estimates:
(A) Unknown inputs
(B) Unmeasured states
(C) System gains
(D) Time constants

24. The state-space model can be derived directly from:
(A) Differential equations
(B) Frequency response data
(C) Bode plots
(D) Nyquist plots

25. The state transition matrix Φ(t) satisfies the property:
(A) Φ(0) = 0
(B) Φ(0) = I
(C) Φ(0) = A
(D) Φ(0) = B

26. The D matrix in a state-space model is zero when:
(A) There is direct feedthrough from input to output
(B) There is no direct feedthrough from input to output
(C) The system is unstable
(D) The system has zeros at origin

27. In discrete-time systems, the state equation is expressed in terms of:
(A) Time derivatives
(B) Difference equations
(C) Integrals
(D) Laplace transforms

28. The state-space model can represent which type of system most accurately?
(A) Only stable systems
(B) Systems with multiple energy storage elements
(C) Purely resistive networks
(D) Time-invariant static systems

29. The solution of the state equation includes two parts:
(A) Steady-state and noise response
(B) Natural and forced response
(C) Static and dynamic response
(D) Step and impulse response

30. The state-space representation provides:
(A) Only steady-state behavior
(B) Complete dynamic behavior of the system
(C) Frequency-domain approximation
(D) Phase-margin analysis