TY - JOUR
T1 - The exponential input-to-state stability property
T2 - characterisations and feedback connections
AU - Guiver, Chris
AU - Logemann, Hartmut
N1 - Funding Information:
We are grateful to three anonymous reviewers, and Prof. Matthew Turner, whose constructive and insightful comments have helped to improve the work. Chris Guiver’s contribution to this work has been partially supported by a Personal Research Fellowship from the Royal Society of Edinburgh (RSE). Chris Guiver expresses gratitude to the RSE for their support.
PY - 2023/1/31
Y1 - 2023/1/31
N2 - 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.
AB - 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.
KW - Differential equation
KW - Exponential input-to-state stability
KW - Feedback connection
KW - Global exponential stability
KW - Robust stability
KW - Small-gain condition
UR - http://www.scopus.com/inward/record.url?scp=85147005850&partnerID=8YFLogxK
U2 - 10.1007/s00498-023-00344-7
DO - 10.1007/s00498-023-00344-7
M3 - Article
AN - SCOPUS:85147005850
JO - Mathematics of Control Signals and Systems
JF - Mathematics of Control Signals and Systems
SN - 0932-4194
ER -