On continuity of solutions for parabolic control systems and input-to-state stability

Birgit Jacob (Corresponding author), Felix L. Schwenninger (Corresponding author), Hans Zwart (Corresponding author)

Onderzoeksoutput: Bijdrage aan tijdschriftTijdschriftartikelAcademicpeer review

2 Citaties (Scopus)

Uittreksel

We study minimal conditions under which mild solutions of linear evolutionary control systems are continuous for arbitrary bounded input functions. This question naturally appears when working with boundary controlled, linear partial differential equations. Here, we focus on parabolic equations which allow for operator-theoretic methods such as the holomorphic functional calculus. Moreover, we investigate stronger conditions than continuity leading to input-to-state stability with respect to Orlicz spaces. This also implies that the notions of input-to-state stability and integral-input-to-state stability coincide if additionally the uncontrolled equation is dissipative and the input space is finite-dimensional.

Originele taal-2Engels
Pagina's (van-tot)6284-6306
Aantal pagina's23
TijdschriftJournal of Differential Equations
Volume266
Nummer van het tijdschrift10
Vroegere onlinedatum8 nov 2018
DOI's
StatusGepubliceerd - 5 mei 2019

Vingerafdruk

Parabolic Systems
Control System
Control systems
Functional Calculus
Orlicz Spaces
Linear partial differential equation
Mild Solution
Partial differential equations
Parabolic Equation
Imply
Arbitrary
Operator

Citeer dit

Jacob, Birgit ; Schwenninger, Felix L. ; Zwart, Hans. / On continuity of solutions for parabolic control systems and input-to-state stability. In: Journal of Differential Equations. 2019 ; Vol. 266, Nr. 10. blz. 6284-6306.
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On continuity of solutions for parabolic control systems and input-to-state stability. / Jacob, Birgit (Corresponding author); Schwenninger, Felix L. (Corresponding author); Zwart, Hans (Corresponding author).

In: Journal of Differential Equations, Vol. 266, Nr. 10, 05.05.2019, blz. 6284-6306.

Onderzoeksoutput: Bijdrage aan tijdschriftTijdschriftartikelAcademicpeer review

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KW - Admissible operator

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KW - H calculus

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