On Exact Controllability of Linear Time Delay Systems of Neutral Type

Rabah, Rabah; Sklyar, Grigory M.

doi:10.1007/978-3-540-49556-7_11

Cited by 2 publications

(2 citation statements)

References 12 publications

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“…The existence of a basis of the state space consisting of eigenvectors (or generalized eigenvectors) essentially simplifies the expression of the moment problem (see [18] and [22]). In our case, the existence of a basis of eigenvectors is determined by the form of the matrix A −1 of the neutral term of the system (1.1), and, in general, such basis does not exist (see [15,16]).…”

Section: Introductionmentioning

confidence: 99%

On Exact Controllability of Time-Delay Systems of Neutral Type

Rabah¹,

Sklyar

Barkhayev

2016

Ukr Math J

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The paper is devoted to the problem of exact controllability for a wide class of neutral and mixed time-delay systems. We consider an equivalent operator model in Hilbert space and formulate steering conditions of controllable states as a vector moment problem. The existence of a basis of eigenvectors of the system operator enables the form of the moment problem to be substantially simplified. A change in control by a feedback law modifies the system structure to guarantee the existence of a basis of eigenvectors of the corresponding operator. We prove a criterion of exact controllability and ascertain the precise critical time of controllability. Анотацiя Робота присвячена вирiшенню задачi точної керованостi для досить широкого класу систем з запiзненням нейтрального та змiшаного типiв. Розглядаючи еквiвалентну операторну модель в гiльбертовому просторi, ми формулюємо умови керованостi у виглядi деякої векторної проблеми моментiв. Вид даної проблеми моментiв iстотно спрощується при наявностi базису простору з власних векторiв оператора системи з запiзненням. Замiна керування дозволяє перетворити структуру системи, i гарантувати iснування базису з власних векторiв вiдповiдного оператора. Ми доводимо критерiй точної керованостi i встановлюємо точний час керування. Аннотация Данная работа посвящена решению задачи точной управляемости для достаточно широкого класса систем с запаздыванием нейтрального и смешанного типов. Рассматривая эквивалентную операторную модель в гильбертовом пространстве, мы формулируем условия управляемости в виде некоторой векторной проблемы моментов. Вид данной проблемы моментов существенно упрощается при наличии базиса пространства из собственных векторов оператора системы с запаздыванием. Замена управления позволяет преобразовать структуру системы, и гарантировать существование базиса из собственных векторов соответствующего оператора. Мы доказываем критерий точной управляемости и устанавливаем точное время управления.

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Section: Introductionmentioning

confidence: 99%

On Exact Controllability of Time-Delay Systems of Neutral Type

Rabah¹,

Sklyar

Barkhayev

2016

Ukr Math J

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“…When there exists a basis of the state space consisting of eigenvectors, the expression of the moment problem is simplified (see Rabah and Sklyar (2007b)). For the system (1), the existence of a basis of generalized eigenvectors is determined by the form of the matrix A −1 .…”

Section: Introductionmentioning

confidence: 99%

The Exact Controllability Property of Neutral Type Systems by the Moment Problem Approach Revisited

Rabah

Sklyar

Barkhayev³

2010

IFAC Proceedings Volumes

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Abstract:In a recent paper authors gave an analysis of the exact controllability problem via the moment problem approach. Namely, the steering conditions of controllable states are formulated as a vectorial moment problem using some Riesz basis. One of the main difficulties was the choice of the basis as, in general, a basis of eigenvectors does not exist. In this contribution we use a change of control by a feedback law and modify the structure of the system in such a way that there exists a basis of eigenvectors which allows a simpler expression of the moment problem. Hence, one obtains the result on exact controllability and on the time of exact controllability.

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On Exact Controllability of Linear Time Delay Systems of Neutral Type

Cited by 2 publications

References 12 publications

On Exact Controllability of Time-Delay Systems of Neutral Type

On Exact Controllability of Time-Delay Systems of Neutral Type

The Exact Controllability Property of Neutral Type Systems by the Moment Problem Approach Revisited

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