Strong input-to-state stability for infinite-dimensional linear systems

Robert Nabiullin; Felix L. Schwenninger

doi:10.1007/s00498-018-0210-8

Strong input-to-state stability for infinite-dimensional linear systems

Robert Nabiullin^*, Felix L. Schwenninger

^*Corresponding author for this work

Research output: Contribution to journal › Article › Academic › peer-review

9 Citations (Scopus)

Abstract

This paper deals with strong versions of input-to-state stability for infinite-dimensional linear systems with an unbounded control operator. We show that strong input-to-state stability with respect to inputs in an Orlicz space is a sufficient condition for a system to be strongly integral input-to-state stable with respect to bounded inputs. In contrast to the special case of systems with exponentially stable semigroup, the converse fails in general.

Original language	English
Article number	4
Journal	Mathematics of Control, Signals, and Systems
Volume	30
Issue number	1
DOIs	https://doi.org/10.1007/s00498-018-0210-8
Publication status	Published - 1 Mar 2018
Externally published	Yes

Keywords

C-semigroup
Infinite-dimensional systems
Infinite-time admissibility
Input-to-state stability
Integral input-to-state stability
Orlicz space

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10.1007/s00498-018-0210-8

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KW - Infinite-time admissibility

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KW - Integral input-to-state stability

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Strong input-to-state stability for infinite-dimensional linear systems

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Keywords

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