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Control SystemsState Space

A continuous-time state-space system x_dot=Ax is asymptotically stable if all eigenvalues of A have?

  • AStrictly negative real parts
  • BStrictly positive real parts
  • CZero real parts only
  • DMagnitude greater than one
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Correct Answer: A. Strictly negative real parts
Explanation: For a finite-dimensional continuous-time LTI system, asymptotic stability requires all eigenvalues of A to lie strictly in the left half-plane.
Reference: Standard control systems: state space
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