Hautus condition on the exact controllability of conservative systems

Zhou, Qi; Yamamoto, Masahiro

doi:10.1080/002071797224162

Cited by 17 publications

(17 citation statements)

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“…As is indicated in Remark 2.1, the strong form of Hautus's test is equivalent to the exact observability for system (1.8) [31]. Now, we show that our weak form of Hautus's test is equivalent to the approximate observability.…”

Section: Dynamic Output Feedback In Control Spacementioning

confidence: 72%

On Stability Equivalence between Dynamic Output Feedback and Static Output Feedback for a Class of Second Order Infinite-Dimensional Systems

Feng¹,

Guo²

2015

SIAM J. Control Optim.

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We consider stabilization for a class of abstract second order infinite-dimensional systems with collocated control and observation. We show that the closed-loop system under a proportional direct output feedback control is asymptotically stable if and only if the closed-loop system under some dynamic output feedback control is asymptotically stable. A Hautus test is developed to ensure the asymptotic stability. Two types of dynamic output feedback controls are investigated. The results are applied to some coupled wave-heat equations where the heat system is considered as a controller of the wave system. This study provides a different view in the study of the coupled systems described by partial differential equations.

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Section: Dynamic Output Feedback In Control Spacementioning

confidence: 72%

On Stability Equivalence between Dynamic Output Feedback and Static Output Feedback for a Class of Second Order Infinite-Dimensional Systems

Feng¹,

Guo²

2015

SIAM J. Control Optim.

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“…Equivalently, it is enough to replace C in (2) by CA −1/2 . To complete the proof of this corollary, we check that Theorem 4.3 applies to this new observation operator (45) and (46) are the needed resolvent conditions. 2…”

Section: Variantsmentioning

confidence: 93%

“…We refer to [25,45,2,27] and to [32] for more background and references. This result was extended to more general groups in [19,Theorem 1.2].…”

Section: Background On Resolvent Conditions For Observabilitymentioning

confidence: 99%

Resolvent conditions for the control of parabolic equations

Duyckaerts

Miller²

2012

Journal of Functional Analysis

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To appear in the Journal of Functional Analysis. 26 pages. Changes: Log function shifted by a unit in (8), (15), (63); paragraph added in the proof of Prop.5.1.b; some rephrasing (mostly in the intro.).International audienceSince the seminal work of Russell and Weiss in 1994, resolvent conditions for various notions of admissibility, observability and controllability, and for various notions of linear evolution equations have been investigated intensively, sometimes under the name of infinite-dimensional Hautus test. This paper sets out resolvent conditions for null-controllability in arbitrary time: necessary for general semigroups, sufficient for analytic normal semigroups. For a positive self-adjoint operator A, it gives a sufficient condition for the null-controllability of the semigroup generated by -A which is only logarithmically stronger than the usual condition for the unitary group generated by iA. This condition is sharp when the observation operator is bounded. The proof combines the so-called ''control transmutation method'' and a new version of the ''direct Lebeau-Robbiano strategy''. The improvement of this strategy also yields interior null-controllability of new logarithmic anomalous diffusions

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“…Therefore the result of Zuazua [16] is generalized. The results of Liu [11] have been extended by Zhou and Yamamoto [15] recently, where general theorems for the exact controtlability of conservative systems ave obtalned.…”

Section: Introductionmentioning

confidence: 99%