Stability of a circuit system

For a circuit represented by the state equation X=AX, the stability is determined by:

• Magnitude of eigenvectors
  
  

• Sign of eigenvalues

• Number of state variables

• Determinant of A

If all eigenvalues of the system matrix A have negative real parts, the circuit is:

• Stable
  

• Unstable

• Marginally stable

• Oscillatory unstable

If the eigenvalues of a circuit system are −2±3i, the behavior is:

• Purely oscillatory

• Marginally stable

• Oscillatory growth
  

• Oscillatory decay

Which of the following eigenvalue conditions corresponds to an unstable circuit?

• Zero eigenvalues only

• All negative real eigenvalues

• One positive real eigenvalue
  

• All eigenvalues purely imaginary

The eigenvector associated with an eigenvalue of the system matrix represents:

• The natural frequency
  

• The mode shape of the system

• The time constant

• The damping factor

In state-space modeling of a 2nd-order RLC circuit, a large value in one component of the eigenvector suggests:

• High oscillation frequency
  

• Faster decay rate

• Dominance of that state variable in the mode

• Critical damping

If all eigenvalues are zero, the system is:

• Stable

• Oscillatory stable

• Unstable

• Marginally stable

For the given matrix the eigenvalues are:

• 1 and 4 ⇒ unstable

• -1 and -4 ⇒ stable

• -1 and 4 ⇒ unstable

• -4 and -1 ⇒ marginally stable

In an RLC circuit, if eigenvalues have positive real parts and imaginary parts, the response will be:

• Pure exponential growth

• Pure exponential decay

• Oscillatory decay

• 
  Oscillatory growth
  

The eigenvalues of a diagonal matrix are:

• The sum of the elements

• The diagonal elements

• Zero

• Undefined