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The exponential input-to-state stability property: characterisations and feedback connections

Guiver, Chris; Logemann, Hartmut


Hartmut Logemann


The exponential input-to-state stability (ISS) property is considered for systems of controlled nonlinear ordinary differential equations. A characterisation of this property is provided, including in terms of a so-called exponential ISS Lyapunov function and a natural concept of linear state/input-to-state L2-gain. Further, the feedback connection of two exponentially ISS systems is shown to be exponentially ISS provided a suitable small-gain condition is satisfied.

Journal Article Type Article
Acceptance Date Jan 10, 2023
Online Publication Date Jan 31, 2023
Publication Date 2023-06
Deposit Date Jan 10, 2023
Publicly Available Date Jan 31, 2023
Print ISSN 0932-4194
Electronic ISSN 1435-568X
Publisher Springer
Peer Reviewed Peer Reviewed
Volume 35
Issue 2
Pages 375-398
Keywords Differential equation, Exponential input-to-state stability, Feedback connection, Global exponential stability, Robust stability, Small-gain condition
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