Laboratory for Control, Learning, and Systems Biology

Papers by L. Grüne and E.D. Sontag

2000
  1. ▪L. Grüne, E.D. Sontag, 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), pp. 850–852, 2000.
    input to state stability
1999
  1. ▪L. Grune, E.D. Sontag, 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, pp. 1220–1225, 1999.
    input to state stability
  2. ▪L. Grüne, E.D. Sontag, F.R. Wirth, "Asymptotic stability equals exponential stability, and ISS equals finite energy gain–if you twist your eyes", Systems Control Lett., vol. 38, no. 2, pp. 127–134, 1999. pdf
    input to state stability · ISS
    Abstract

    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.