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Advanced, Contemporary Control pp 1132–1140Cite as

Controllability of Higher Order Linear Systems with Multiple Delays in Control

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Part of the book series: Advances in Intelligent Systems and Computing ((AISC,volume 1196))

Abstract

In the present chapter finite-dimensional dynamical control systems described by linear higher-order ordinary differential state equations with multiple point delays in control are considered. Using algebraic methods, necessary and sufficient conditions for relative controllability in a given time interval for linear dynamical system with multiple point delays in control are formulated and proved. This condition is generalization to relative controllability case some previous results concerning controllability of linear dynamical systems without multiple point delays in the control. Proof of the main result is based on necessary and sufficient controllability condition for linear systems without delays in control. Simple numerical example, which illustrates theoretical result is also given. Finally, some remarks and comments on the existing results for controllability of dynamical systems with delays in control are also presented.

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References

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Acknowledgment

The work is supported by National Science Centre in Poland under grant: “Modelling, optimization and control for structural reduction of device noise”, DEC-2017/25/B/ST7/02236.

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Authors and Affiliations

  1. Silesian University of Technology, 44-100, Gliwice, Poland

    Jerzy Klamka

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  1. Jerzy Klamka
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Correspondence to Jerzy Klamka .

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Editors and Affiliations

  1. Institute of Automatic Control, Lodz University of Technology, Lodz, Poland

    Andrzej Bartoszewicz

  2. Institute of Automatic Control, Lodz University of Technology, Lodz, Poland

    Jacek Kabziński

  3. Systems Research Institute, Polish Academy of Sciences, Warsaw, Poland

    Janusz Kacprzyk

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Klamka, J. (2020). Controllability of Higher Order Linear Systems with Multiple Delays in Control. In: Bartoszewicz, A., Kabziński, J., Kacprzyk, J. (eds) Advanced, Contemporary Control. Advances in Intelligent Systems and Computing, vol 1196. Springer, Cham. https://doi.org/10.1007/978-3-030-50936-1_94

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