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Approximation of nonlinear systems having outputs

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Abstract

Suppose we have a nonlinear system with output

$$\begin{gathered} \dot x = f(x) + g(x)u, \hfill \\ y = h(x), \hfill \\ \end{gathered}$$

an open setO of state spaceR n, and a positive integerk. We find conditions onf,g, andh so that for eachx 0 ε O there is ann-dimensional affine linear system, which depends onx 0 but not onu, having the property that the output time responses (starting at the statex 0 of the original nonlinear system and this approximating linear system agree through orderk for any admissable controlu. Several possible applications of our results are examined.

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References

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Authors and Affiliations

  1. Programs in Mathematical Sciences, The University of Texas at Dallas, 75083-0688, Richardson, TX, USA

    L. R. Hunt

  2. Department of Electrical Engineering, Texas Tech University, 79409, Lubbock, TX, USA

    Renjeng Su

Authors
  1. L. R. Hunt
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  2. Renjeng Su
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Additional information

This research was supported by NASA Ames Research Office under Grants NAG 2-366 and NAG 2-203.

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Hunt, L.R., Su, R. Approximation of nonlinear systems having outputs. Circuits Systems and Signal Process 5, 465–479 (1986). https://doi.org/10.1007/BF01599621

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  • DOI: https://doi.org/10.1007/BF01599621

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