The sensitivity of the stable Lyapunov equation

@article{Hewer1987TheSO,
  title={The sensitivity of the stable Lyapunov equation},
  author={Gary A. Hewer and Charles S. Kenney},
  journal={26th IEEE Conference on Decision and Control},
  year={1987},
  volume={26},
  pages={2122-2122}
}
An analysis is presented of the sensitivity of the solution of the Lyapunov equation A*X + XA = -W, where A is stable. This analysis leads to a spectral norm bound on the relative perturbation of the solution which is optimal for a certain class of estimates and which is essentially equivalent to the Frobenius norm bound obtained from the associated Kronecker product system. The latter bound can be expressed in terms of sep(A*, -A) and is known to accurately reflect the sensitivity of the… CONTINUE READING
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