On the admissibility of observation for perturbed -semigroups on Banach spaces

Hadd, Saïd; Idrissi, Abdelali

doi:10.1016/j.sysconle.2005.04.010

Cited by 29 publications

(34 citation statements)

References 16 publications

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“…Sometimes, if A generates a C 0 -semigroup on the state space and the admissibility of the control operator (or observation operator) for A is easy to check, we can write the generator of semigroup of the system as a sum of two simple operators, (A −1 + ΔA)| X (or A + P ). Thus the perturbation method can be used to test the admissible for the considered generator of semigroup of the system (see [8,9]). …”

Section: Introductionmentioning

confidence: 99%

“…Clearly, output feedback can be regarded as an perturbation [31]. However, in practical applications, it is hard to check that whether an infinite dimensional system is the feedback of another one or not; in contrast, it is easier to decompose the generator of semigroup of the system into a sum of two operators as in [8,9]. Motivated by this, in this paper, we consider the later scheme.…”

Section: Introductionmentioning

confidence: 99%

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On the Perturbations of Regular Linear Systems and Linear Systems with State and Output Delays

Mei

Peng

2010

Integr. Equ. Oper. Theory

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This paper is concerned with perturbation problems of regularity linear systems. Two types of perturbation results are proved: (i) the perturbed system (A + P, B, C) generates a regular linear system provided both (A, B, C) and (A, B, P ) generate regular linear systems; and (ii) the perturbed system ((A−1 + ΔA)|X , B, C A Λ ) generates a regular linear system if both (A, B, C) and (A, ΔA, C) generate regular linear systems. These allow us to establish a new variation of constants formula of the control system (A + P, B). Moreover, these results are applied to the linear systems with state and output delays. The regularity and the mild expressibility is deduced, and a necessary and sufficient condition for stabilizability of the delayed systems is proved.Mathematics Subject Classification (2010). Primary 47A55; Secondary 93C23.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

On the Perturbations of Regular Linear Systems and Linear Systems with State and Output Delays

Mei

Peng

2010

Integr. Equ. Oper. Theory

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“…Moreover, he proved in [6,8] [6] and [24] are concerned with the admissible control perturbation to exact controllability and the admissible observation perturbation to exact observability, respectively. To the best of the authors' knowledge, for unbounded generator, control and observation operators, there is no literature which discusses the cross perturbations, that is, admissible control perturbation to exact observability and admissible observation perturbation to exact controllability (in fact, the work of [14] can be regarded as cross perturbation for the bounded control operator).…”

Section: T −1 (T − S)bu(s)ds Is Continuous Frommentioning

confidence: 99%

On robustness of exact controllability and exact observability under cross perturbations of the generator in Banach spaces

Mei

Peng

2010

Proc. Amer. Math. Soc.

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Abstract. This paper is concerned with the exact controllability and exact observability of linear systems in the Banach space setting. It is proved that both the admissibility of control operators and the admissibility of observation operators are invariant to cross perturbations of the generator of a C 0 -semigroup. Moreover, under the admissibility invariance premise, the robustness of the exact controllability as well as the exact observability to such cross perturbations is verified. An illustrative example is presented.

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“…this is equivalent to prove feedback stabilizability of the open-loop system (13). To that purpose, we need some information on the spectrum σ(A).…”

Section: Feedback Stabilizability Of Neutral Systemsmentioning

confidence: 99%

“…Proof: As we have seen instead of the neutral system (1) one can consider the open-loop system (A, B) described by (13), which we assume that it is feedback stabilizable. According to [5], there exists δ > 0 such that…”

Section: Feedback Stabilizability Of Neutral Systemsmentioning

confidence: 99%

Feedback stabilizability of infinite dimensional neutral systems

Hadd

Nounou

2010

49th IEEE Conference on Decision and Control (CDC)

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Abstract-A new functional analytic approach to the concept of feedback stabilizability of infinite dimensional linear neutral systems is presented. We first reformulate this systems as an infinite dimensional open-loop systems with appropriate semigroups and unbounded control operators. We introduce conditions for which such semigroups are eventually compact. In addition, when the image of the control operator is finite dimensional, we give necessary and sufficient conditions for the feedback stabilizability of neutral system. Our approach is based on the concept of regular linear systems in the Salamon-Weiss sens.

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On the admissibility of observation for perturbed -semigroups on Banach spaces

Cited by 29 publications

References 16 publications

On the Perturbations of Regular Linear Systems and Linear Systems with State and Output Delays

On the Perturbations of Regular Linear Systems and Linear Systems with State and Output Delays

On robustness of exact controllability and exact observability under cross perturbations of the generator in Banach spaces

Feedback stabilizability of infinite dimensional neutral systems

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