Lyapunov Measure for Almost Everywhere Stability

  title={Lyapunov Measure for Almost Everywhere Stability},
  author={Umesh Vaidya and Prashant G. Mehta},
  journal={IEEE Transactions on Automatic Control},
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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Showing 1-10 of 40 references

A dual to Lyapunov’s stability theorem,

  • A. Rantzer
  • Syst. Control Lett.,
  • 2001
Highly Influential
5 Excerpts

Markov Chains and Stochastic Stability

  • S. P. Meyn, R. L. Tweedie
  • Berlin, Germany: Springer-Verlag
  • 1993
Highly Influential
5 Excerpts

Nonquadratic Lyapunov functions for robust stability analysis of linear uncertain systems

  • A. L. Zelentovsky
  • Positive Polynomials in Control ( Lecture Notes…
  • 2005

The algorithms behind GAIO — Set oriented numerical methods for dynamical systems

  • G. Froyland M. Dellnitz, O. Junge
  • Ergodic Theory , Analysis , and Efficient…
  • 2005

Comparison of systems with complex behavior,

  • I. Mezic, A. Banaszuk
  • Phys. D,
  • 2004
1 Excerpt

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