Controllability of Higher Order Linear Systems with Multiple Delays in Control

Jerzy Klamka

doi:10.1007/978-3-030-50936-1_94

Controllability of Higher Order Linear Systems with Multiple Delays in Control

Jerzy Klamka

Department of Measurements and Control Systems (RAU/RAU2)

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

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.

Original language	English
Title of host publication	Advanced, Contemporary Control - Proceedings of KKA 2020—The 20th Polish Control Conference, 2020
Editors	Andrzej Bartoszewicz, Jacek Kabzinski, Janusz Kacprzyk
Publisher	Springer
Pages	1132-1140
Number of pages	9
ISBN (Print)	9783030509354
DOIs	https://doi.org/10.1007/978-3-030-50936-1_94
Publication status	Published - 2020
Event	20th Polish Control Conference, PCC 2020 - Lodz, Poland Duration: 22 Jun 2020 → 24 Jun 2020

Publication series

Name	Advances in Intelligent Systems and Computing
Volume	1196 AISC
ISSN (Print)	2194-5357
ISSN (Electronic)	2194-5365

Conference

Conference	20th Polish Control Conference, PCC 2020
Country/Territory	Poland
City	Lodz
Period	22/06/20 → 24/06/20

Keywords

Controllability
Higher order systems
Linear systems

ASJC Scopus subject areas

Control and Systems Engineering
General Computer Science

Access to Document

10.1007/978-3-030-50936-1_94

Cite this

Klamka, J. (2020). Controllability of Higher Order Linear Systems with Multiple Delays in Control. In A. Bartoszewicz, J. Kabzinski, & J. Kacprzyk (Eds.), Advanced, Contemporary Control - Proceedings of KKA 2020—The 20th Polish Control Conference, 2020 (pp. 1132-1140). (Advances in Intelligent Systems and Computing; Vol. 1196 AISC). Springer. https://doi.org/10.1007/978-3-030-50936-1_94

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title = "Controllability of Higher Order Linear Systems with Multiple Delays in Control",

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.",

keywords = "Controllability, Higher order systems, Linear systems",

author = "Jerzy Klamka",

note = "Publisher Copyright: {\textcopyright} 2020, Springer Nature Switzerland AG.; 20th Polish Control Conference, PCC 2020 ; Conference date: 22-06-2020 Through 24-06-2020",

year = "2020",

doi = "10.1007/978-3-030-50936-1\_94",

language = "English",

isbn = "9783030509354",

series = "Advances in Intelligent Systems and Computing",

publisher = "Springer",

pages = "1132--1140",

editor = "Andrzej Bartoszewicz and Jacek Kabzinski and Janusz Kacprzyk",

booktitle = "Advanced, Contemporary Control - Proceedings of KKA 2020{\textemdash}The 20th Polish Control Conference, 2020",

address = "Germany",

}

Klamka, J 2020, Controllability of Higher Order Linear Systems with Multiple Delays in Control. in A Bartoszewicz, J Kabzinski & J Kacprzyk (eds), Advanced, Contemporary Control - Proceedings of KKA 2020—The 20th Polish Control Conference, 2020. Advances in Intelligent Systems and Computing, vol. 1196 AISC, Springer, pp. 1132-1140, 20th Polish Control Conference, PCC 2020, Lodz, Poland, 22/06/20. https://doi.org/10.1007/978-3-030-50936-1_94

Controllability of Higher Order Linear Systems with Multiple Delays in Control. / Klamka, Jerzy.
Advanced, Contemporary Control - Proceedings of KKA 2020—The 20th Polish Control Conference, 2020. ed. / Andrzej Bartoszewicz; Jacek Kabzinski; Janusz Kacprzyk. Springer, 2020. p. 1132-1140 (Advances in Intelligent Systems and Computing; Vol. 1196 AISC).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

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AU - Klamka, Jerzy

PY - 2020

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N2 - 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.

AB - 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.

KW - Controllability

KW - Higher order systems

KW - Linear systems

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DO - 10.1007/978-3-030-50936-1_94

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PB - Springer

T2 - 20th Polish Control Conference, PCC 2020

Y2 - 22 June 2020 through 24 June 2020

ER -

Controllability of Higher Order Linear Systems with Multiple Delays in Control

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