Publications of Eduardo D. Sontag jointly with L. Grune
Articles in journal or book chapters
  1. L. Grüne, E.D. Sontag, and F.R. Wirth. On equivalence of exponential and asymptotic stability under changes of variables. In International Conference on Differential Equations, Vol. 1, 2 (Berlin, 1999), pages 850-852. World Sci. Publishing, River Edge, NJ, 2000. Keyword(s): input to state stability.

  2. L. Grüne, E.D. Sontag, and F.R. Wirth. Asymptotic stability equals exponential stability, and ISS equals finite energy gain---if you twist your eyes. Systems Control Lett., 38(2):127-134, 1999. [PDF] Keyword(s): input to state stability, ISS.
    This paper shows that uniformly global asymptotic stability for a family of ordinary differential equations is equivalent to uniformly global exponential stability under a suitable nonlinear change of variables. The same is shown respectively for input-to-state stability, input-to-state exponential stability, and the property of finite square-norm gain ("nonlinear H-infty"). The results are shown for systems of any dimension not equal to 4 or 5.

Conference articles
  1. L. Grune, E.D. Sontag, and F.R. Wirth. On the equivalence between asymptotic and exponential stability, and between ISS and finite H infinity gain. In Proc. IEEE Conf. Decision and Control, Phoenix, Dec. 1999, IEEE Publications, 1999, pages 1220-1225, 1999. Keyword(s): input to state stability.



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Last modified: Wed Apr 17 19:59:02 2024
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