A linear dynamic feedback controller for non-linear systems described by matrix differential equations of the second and first orders

A linear dynamic feedback controller for non-linear systems described by matrix differential equations of the second and first orders

The paper presents a design scheme of the linear dynamic feedback controller for some non-linear systems. These systems are mathematically described by matrix non-linear differential equations of the first and second orders. A first-order form of the studied systems includes some types of differenti...

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Main Authors: Paweł Skruch, Marek Długosz
Format: Article
Language:English
Published: SAGE Publishing 2019-09-01
Series:Measurement + Control
Online Access:https://doi.org/10.1177/0020294019834964
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spelling doaj-fcfcda5ce9254428a5006cd8ab41dc462020-11-25T03:54:00ZengSAGE PublishingMeasurement + Control0020-29402019-09-015210.1177/0020294019834964A linear dynamic feedback controller for non-linear systems described by matrix differential equations of the second and first ordersPaweł SkruchMarek DługoszThe paper presents a design scheme of the linear dynamic feedback controller for some non-linear systems. These systems are mathematically described by matrix non-linear differential equations of the first and second orders. A first-order form of the studied systems includes some types of differential-algebraic equations. The stability property of the non-linear systems with the linear controller is assured by an appropriate definition of the system output, and the linear dynamic compensator is an important part of the feedback control system. The order of the dynamic part is equal to the size of the system input and is independent of the size of the system state vector. The asymptotic stability in the Lyapunov sense is analysed and proved by the use of Lyapunov functionals and LaSalle’s invariance principle. Stabilisation in a wide range of controller parameters improves the system’s robustness.https://doi.org/10.1177/0020294019834964
collection DOAJ
language English
format Article
sources DOAJ
author Paweł Skruch
Marek Długosz
spellingShingle Paweł Skruch
Marek Długosz
A linear dynamic feedback controller for non-linear systems described by matrix differential equations of the second and first orders
Measurement + Control
author_facet Paweł Skruch
Marek Długosz
author_sort Paweł Skruch
title A linear dynamic feedback controller for non-linear systems described by matrix differential equations of the second and first orders
title_short A linear dynamic feedback controller for non-linear systems described by matrix differential equations of the second and first orders
title_full A linear dynamic feedback controller for non-linear systems described by matrix differential equations of the second and first orders
title_fullStr A linear dynamic feedback controller for non-linear systems described by matrix differential equations of the second and first orders
title_full_unstemmed A linear dynamic feedback controller for non-linear systems described by matrix differential equations of the second and first orders
title_sort linear dynamic feedback controller for non-linear systems described by matrix differential equations of the second and first orders
publisher SAGE Publishing
series Measurement + Control
issn 0020-2940
publishDate 2019-09-01
description The paper presents a design scheme of the linear dynamic feedback controller for some non-linear systems. These systems are mathematically described by matrix non-linear differential equations of the first and second orders. A first-order form of the studied systems includes some types of differential-algebraic equations. The stability property of the non-linear systems with the linear controller is assured by an appropriate definition of the system output, and the linear dynamic compensator is an important part of the feedback control system. The order of the dynamic part is equal to the size of the system input and is independent of the size of the system state vector. The asymptotic stability in the Lyapunov sense is analysed and proved by the use of Lyapunov functionals and LaSalle’s invariance principle. Stabilisation in a wide range of controller parameters improves the system’s robustness.
url https://doi.org/10.1177/0020294019834964
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AT marekdługosz alineardynamicfeedbackcontrollerfornonlinearsystemsdescribedbymatrixdifferentialequationsofthesecondandfirstorders
AT pawełskruch lineardynamicfeedbackcontrollerfornonlinearsystemsdescribedbymatrixdifferentialequationsofthesecondandfirstorders
AT marekdługosz lineardynamicfeedbackcontrollerfornonlinearsystemsdescribedbymatrixdifferentialequationsofthesecondandfirstorders
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