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Carleman Linearization of Linearly Observable Polynomial Systems

In: Mathematical Control Theory and Finance

Author

Listed:
  • Dorota Mozyrska

    (Białystok Technical University, Faculty of Computer Science)

  • Zbigniew Bartosiewicz

    (Białystok Technical University, Faculty of Computer Science)

Abstract

Summary Carleman linearization is used to transform a polynomial control system with output, defined on n-dimensional space, into a linear or bilinear system evolving in the space of infinite sequences. Such a system is described by infinite matrices with special properties. Linear observability of the original system is studied. It means that all coordinate functions can be expressed as linear combinations of functions from the observation space. It is shown that this property is equivalent to a rank condition involving matrices that appear in the Carleman linearization. This condition is equivalent to observability of the first n coordinates of the linearized system.

Suggested Citation

  • Dorota Mozyrska & Zbigniew Bartosiewicz, 2008. "Carleman Linearization of Linearly Observable Polynomial Systems," Springer Books, in: Andrey Sarychev & Albert Shiryaev & Manuel Guerra & Maria do Rosário Grossinho (ed.), Mathematical Control Theory and Finance, pages 311-323, Springer.
    • Handle: RePEc:spr:sprchp:978-3-540-69532-5_17
    DOI: 10.1007/978-3-540-69532-5_17
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