Abstract
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.
| Original language | English |
|---|---|
| Pages (from-to) | 6284-6306 |
| Number of pages | 23 |
| Journal | Journal of Differential Equations |
| Volume | 266 |
| Issue number | 10 |
| Early online date | 8 Nov 2018 |
| DOIs | |
| Publication status | Published - 5 May 2019 |
Funding
The authors are very grateful to Jonathan R. Partington for fruitful discussions on the content of the article. They would like to thank Bernhard Haak for helpful comments on the Weiss conjecture for L p . The first and the second named author received funding from the Deutsche Forschungsgemeinschaft (DFG) , grant number JA 735/12-1 . The second named author is further supported by the DFG , grant number RE 2917/4-1 . The support is greatly acknowledged. Finally the authors are very thankful to the anonymous referees for their careful reading and helpful suggestions. Appendix A
Keywords
- Abstract parabolic control system
- Admissible operator
- Bounded functional calculus
- H calculus
- Input-to-state stability
- Orlicz space
Fingerprint
Dive into the research topics of 'On continuity of solutions for parabolic control systems and input-to-state stability'. Together they form a unique fingerprint.Cite this
- APA
- Author
- BIBTEX
- Harvard
- Standard
- RIS
- Vancouver