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Publications of Eduardo D. Sontag jointly with M. Lang
Articles in journal or book chapters
  1. M. Lang and E.D. Sontag. Zeros of nonlinear systems with input invariances. Automatica, 81:46-55, 2017. [PDF] Keyword(s): scale invariance, fold change detection, nonlinear systems, realization theory, internal model principle.
    Abstract:
    This paper introduces two generalizations of systems invariant with respect to continuous sets of input transformations, that is, systems whose output dynamics remain invariant when applying a transformation to the input and simultaneously adjusting the initial conditions. These generalizations concern systems invariant with respect to time-dependent input transformations with exponentially increasing or decreasing ``strength'', and systems invariant with respect to transformations of the "nonlinear derivatives" of the input. Interestingly, these two generalizations of invariant systems encompass linear time-invariant (LTI) systems with real transfer function zeros of arbitrary multiplicity. Furthermore, the zero-dynamics of systems possessing our generalized invariances show properties analogous to those of LTI systems with transfer function zeros, generalizing concepts like pole-zero cancellation, the rejection of ramps by Hurwitz LTI systems with a zero at the origin with multiplicity two, and (to a certain extend) the superposition principle with respect to inputs zeroing the output.


Conference articles
  1. M. Lang and E.D. Sontag. Scale-invariant systems realize nonlinear differential operators. In 2016 American Control Conference (ACC), pages 6676 - 6682, 2016. [PDF] Keyword(s): scale invariance, fold change detection, nonlinear systems, realization theory, internal model principle.
    Abstract:
    In this article, we show that scale-invariant systems, as well as systems invariant with respect to other input transformations, can realize nonlinear differential operators: when excited by inputs obeying functional forms characteristic for a given class of invariant systems, the systems' outputs converge to constant values directly quantifying the speed of the input.



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Last modified: Thu Nov 23 10:40:56 2017
Author: sontag.


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