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)

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20 Citaten (Scopus)
3 Downloads (Pure)


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
Nummer van het tijdschrift10
Vroegere onlinedatum8 nov 2018
StatusGepubliceerd - 5 mei 2019


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