Input-to-state dynamical stability and its Lyapunov function characterization

We present a new variant of the input-to-state stability (ISS) property which is based on using a one-dimensional dynamical system for building the class 𝒦L function for the decay estimate and for describing the influence of the perturbation. We show the relation to the original ISS formulation and describe characterizations by means of suitable Lyapunov functions. As applications, we derive quantitative results on stability margins for nonlinear systems and a quantitative version of a small gain theorem for nonlinear systems.