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Original Articles

Robust stability analysis using Lyapunov density

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Pages 1077-1085 | Received 24 Aug 2012, Accepted 04 Feb 2013, Published online: 09 Apr 2013

References

  • Angeli, D. (2003). Some remarks on density functions for dual Lyapunov methods. Proceedings of the 42nd IEEE CDC (pp. 5080–5082).
  • Khalil, H. K. (1996). Nonlinear systems. New Jersey: Prentice Hall.
  • Lasota, A., & Mackey, M. C. (1994). Chaos, fractals, and noise: Stochastic aspects of dynamics. New York: Springer-Verlag.
  • Prajna, S., Parrilo, P. A., & Rantzer, A. (2004). Nonlinear control synthesis by convex optimization. IEEE Transactions on Automatic Control, 49, 1–5.
  • Prajna, S., & Rantzer, A. (2003). On homogeneous density functions. In A. Rantzer & C.I. Byrnes, Lecture notes in control and information sciences, Vol. 286, Directions in Mathematical Systems Theory and Optimization (pp. 261–274). New York: Springer-Verlag.
  • Rajaram, R., Vaidya, U., & Fardad, M. (2007). Connection between almost everywhere stability and advection PDE. Manuscript submitted to IEEE Conference on Decision and Control for publication.
  • Rajaram, R., Vaidya, U., Fardad, M., & Ganapathysubramanian, G. (2010). Stability in the almost everywhere sense: A linear transfer operator approach. Journal of Mathematical Analysis and Applications, 368, 677–691.
  • Rantzer, A. (2001). A dual to Lyapunov’s stability theorem. Systems & Control Letters, 42, 161–168.
  • Rantzer, A. (2002). A Converse theorem for density functions. Proceedings of IEEE Conference on Decision and Control (pp. 1890–1891).
  • Vaidya, U. (2007). Converse theorem for almost everywhere stability using Lyapunov measure. Proceedings of American Control Conference (pp. 4835–4840).
  • Vaidya, U., & Mehta, P.G. (2008). Lyapunov measure for almost everywhere stability. IEEE Transactions on Automatic Control, 53, 307–323.

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