Lyapunov Measure for Almost Everywhere Stability

@article{Vaidya2008LyapunovMF,
  title={Lyapunov Measure for Almost Everywhere Stability},
  author={Umesh Vaidya and Prashant G. Mehta},
  journal={IEEE Transactions on Automatic Control},
  year={2008},
  volume={53},
  pages={307-323}
}
This paper is concerned with the analysis and computational methods for verifying global stability of an attractor set of a nonlinear dynamical system. Based upon a stochastic representation of deterministic dynamics, a Lyapunov measure is proposed for these purposes. This measure is shown to be a stochastic counterpart of stability (transience) just as an invariant measure is a counterpart of the attractor (recurrence). It is a dual of the Lyapunov function and is useful for the study of more… CONTINUE READING
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