Criteria for Function Space Controllability of Linear Neutral Systems

Jacobs, Marc Q.; Langenhop, C. E.

doi:10.1137/0314064

Cited by 45 publications

(21 citation statements)

References 16 publications

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“…It is shown that when the controls of a neutral functional differential system with infinite delays are restrained to lie in the unit cube, the requirements for null controllability are that the system has full rank with the condition that ( ) (exp(− ℎ)) ≠ 0 and an additional condition that the trivial solution of the uncontrolled system be uniformly asymptotically stable. The results obtained by this method will extend that of (Underwood and Chukwu, 1988;Jacobs and Langenhop, 1976;Rivera Rodas and Langenhop, 1978) to neutral functional differential system having infinite delays by using the Schauder fixed point theorem. The rest of the paper is organised as follows.…”

Section: Introductionmentioning

confidence: 66%

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Null controllability of neutral system with infinite delays

Davies

Haas

2015

European Journal of Control

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Sufficient conditions are developed for the null controllability of neutral control systems with infinite delay when the values of the control lie in an -dimensional unit cube. Conditions are placed on the perturbation function which guarantee that; if the uncontrolled system is uniformly asymptotically stable and the control system satisfies a full rank condition so that ( ) (exp(− ℎ)) ≠ 0, for every complex , where ( ) is an × polynomial matrix in constructed from the coefficient matrices of the control system and (exp(− ℎ)) is the transpose of [1, exp(− ℎ) , ⋯ , exp(−( − 1) ℎ)], then the control system is null controllable with constraint.

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Section: Introductionmentioning

confidence: 66%

“…This section develops and proves necessary and sufficient controllability conditions for systems (3) by exploiting the method in (Jacobs and Langenhop, 1976;Rivera Rodas and Langenhop, 1978). Some relevant controllability results which are relevant to this study are also given.…”

Section: Controllability Resultsmentioning

confidence: 99%

Null controllability of neutral system with infinite delays

Davies

Haas

2015

European Journal of Control

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“…The main non trivial precision is the time of controllability. We generalize the results given [6] for the case of a single input and one localized delay (see also [2,14]). The approach developed here is different from that of [9].…”

Section: Introductionmentioning

confidence: 67%

On Exact Controllability of Linear Time Delay Systems of Neutral Type

Rabah¹,

Sklyar

2007

Applications of Time Delay Systems

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To cite this version:Rabah Rabah, Grigory Sklyar. On exact controllability of linear time delay systems of neutral type. Summary. The problem of exact null controllability is considered for linear neutral type systems with distributed delay. A characterization of this problem is given. The minimal time of controllability is precised. The results are based on the analysis of the Riesz basis property of eigenspaces in Hilbert space. Recent results on the moment problem and properties of exponential families are used.

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“…This may be very important in the problem of time minimal problem and other related problems of optimal control. In this case the semigroup is not explicitly known in contrast to the situation of several discrete delays (see O'Connor and Tarn (1983);Jacobs and Langenhop (1976); Banks et al (1975);Rivera Rodas and Langenhop (1978)). To study controllability we use the moment problem approach.…”

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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Criteria for Function Space Controllability of Linear Neutral Systems

Cited by 45 publications

References 16 publications

Null controllability of neutral system with infinite delays

Null controllability of neutral system with infinite delays

On Exact Controllability of Linear Time Delay Systems of Neutral Type

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

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