The differentiation index of nonlinear differential-algebraic equations versus the relative degree of nonlinear control systems

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It is claimed in [1] that the notion of the relative degree in nonlinear control theory is closely related to that of the differentiation index for nonlinear differential-algebraic equations (DAEs). In this paper, we give more insights on this claim via a recent proposed concept (see [2]) called the explicitation of DAEs. The explicitation attaches a class of control systems to a given DAE, we show that the relative degree of the systems in the explicitation class is invariant in some sense and that the differentiation index of the original DAE coincides with the maximum of the relative degree of the explicitation systems.
Original languageEnglish
Title of host publication91st Annual Meeting of the International Association of Applied Mathematics and Mechanics (GAMM)
EditorsD. Kuhl, A. Meister, A. Ricoeur, O. Wünsch
Number of pages3
Publication statusPublished - Jan-2021

Publication series

PublisherJohn Wiley & Sons, Ltd
ISSN (Print)1617-7061

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