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

Guiver, Chris; Logemann, Hartmut

Abstract

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.

Citation

Guiver, C., & Logemann, H. (2023). The exponential input-to-state stability property: characterisations and feedback connections. Mathematics of Control, Signals, and Systems, 35(2), 375-398. https://doi.org/10.1007/s00498-023-00344-7

• 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
• DOI: https://doi.org/10.1007/s00498-023-00344-7
• Keywords: Differential equation, Exponential input-to-state stability, Feedback connection, Global exponential stability, Robust stability, Small-gain condition
• Publisher URL: https://www.springer.com/journal/498