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On a generalization of relative degree

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Abstract

We generalize the notion of relative degree for a controlled dynamical system (possibly, discrete). We show that the new notion of leading incomplete relative degree is uniquely determined for a broad class of “square” dynamical systems (i.e., systems with as many inputs as outputs), including controllable systems. If r is the vector of relative degree of a system in the classical sense, then it is so in the generalized sense as well. We indicate a constructive algorithm for computing the leading incomplete relative degree.

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References

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Authors and Affiliations

  1. Moscow State University, Moscow, Russia

    A. V. Kraev, A. I. Rogovskii & V. V. Fomichev

  2. Institute for Systems Analysis, Russian Academy of Sciences, Moscow, Russia

    A. V. Kraev, A. I. Rogovskii & V. V. Fomichev

  3. Institute of Control Problems, Russian Academy of Sciences, Moscow, Russia

    A. V. Kraev, A. I. Rogovskii & V. V. Fomichev

Authors
  1. A. V. Kraev
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  2. A. I. Rogovskii
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  3. V. V. Fomichev
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Corresponding author

Correspondence to A. V. Kraev.

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Original Russian Text © A.V. Kraev, A.I. Rogovskii, V.V. Fomichev, 2014, published in Differentsial’nye Uravneniya, 2014, Vol. 50, No. 8, pp. 1128–1132.

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Kraev, A.V., Rogovskii, A.I. & Fomichev, V.V. On a generalization of relative degree. Diff Equat 50, 1122–1127 (2014). https://doi.org/10.1134/S0012266114080102

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  • DOI: https://doi.org/10.1134/S0012266114080102

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