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

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 L^2-gain. Further, the feedback connection of two exponentially ISS systems is shown to be exponentially ISS provided a suitable small-gain condition is satisfied.