Robustness of controllability under some unbounded perturbations

Boulite, S.; Idrissi, Abdelali; Maniar, Lahcen

doi:10.1016/j.jmaa.2004.09.035

Cited by 14 publications

(8 citation statements)

References 5 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…So, to conclude the theorem, it is sufficient to show that W A,C is completed under some norm · W A,C (τ ) . In the same way as with the proof of [9, Proposition 1], we can show that W A,C is a Banach space for the norm R W A,C (1) , as expected.…”

Section: Proof By Lemma 32 and Lemma 34 It Follows That ∀τ τsupporting

confidence: 76%

“…To complete the proof, it suffices to show that R A,B is complete under some norm R R A,B (τ ) . Similarly to the proof of [9, Proposition 1], it is easy to show that R A,B is a Banach space under the norm R R A,B (1) .…”

Section: Y ) : (A B R) Generates a Regular Linear System} Is A Banamentioning

confidence: 86%

“…The arguments used in [1] relies heavily on estimates using Dyson-Phillips series, involving calculations facilitated only by the boundedness of the control operator on X. However, in partial differential equations the control usually acts on the boundary.…”

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

confidence: 99%

“…Such systems can be reformulated as distributed control systems of the forṁ x(t) = Ax(t)+Bu (t), where the control operator is strictly unbounded (see [17,21]). These cases are beyond the scope of [1] and [14] which considered the case that the control operator B is bounded. Dual to control, the observation is usually of point evaluation, and thereby unbounded.…”

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

confidence: 99%

See 3 more Smart Citations

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

Mei

Peng

2010

Proc. Amer. Math. Soc.

View full text Add to dashboard Cite

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.

show abstract

Section: Proof By Lemma 32 and Lemma 34 It Follows That ∀τ τsupporting

confidence: 76%

Section: Y ) : (A B R) Generates a Regular Linear System} Is A Banamentioning

confidence: 86%

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

confidence: 99%

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

confidence: 99%

See 2 more Smart Citations

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

Mei

Peng

2010

Proc. Amer. Math. Soc.

View full text Add to dashboard Cite

show abstract

“…The remaining of the proof follows the proof of Boulite et al[2, Proposition 4]. Now, we can state the main result of this section as follows.Theorem 5.6.…”

mentioning

confidence: 64%

Admissibility and Observability of Observation Operators for Semilinear Problems

Baroun

Jacob

2009

Integr. equ. oper. theory

View full text Add to dashboard Cite

This paper deals with semilinear evolution equations with unbounded observation operators. Sufficient conditions are given guaranteeing that the output function of a semilinear system is in L 2 loc ([0, ∞); Y ). We prove that the Lebesgue extension of the observation operators are invariant under nonlinear globally Lipschitz continuous perturbations. Further, relations between the corresponding Λ-extensions are studied. We show that exact observability of linear autonomous system is conserved under small Lipschitz perturbations. The obtained results are illustrated by several examples. (2000). Primary 47H20; Secondary 93C73, 93B07, 93C25. Mathematics Subject Classification

show abstract

Robustness of Exact p‐Controllability and Exact p‐Observability to q‐Type of Perturbations of the Generator

Mei¹,

Peng²

2013

Asian Journal of Control

View full text Add to dashboard Cite

In Mei and Peng, Systems & Control Letters, 59 (2010) 470–475, the authors have proved in general setting that p‐admissibilities of control operators and observation operators are invariant to any q‐type of perturbations of generator of C0‐semigroups on Banach space. In this paper, under the p‐admissibility invariance premise, the robustness of the exact p‐controllability as well as the exact p‐observability to q‐type of perturbations is verified.

show abstract

Robustness of controllability under some unbounded perturbations

Cited by 14 publications

References 5 publications

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

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

Admissibility and Observability of Observation Operators for Semilinear Problems

Robustness of Exact p‐Controllability and Exact p‐Observability to q‐Type of Perturbations of the Generator

Contact Info

Product

Resources

About