Minimum integral input-to-state stability bounds

Integral input-to-state stability (iISS) is a robust stability property of interest in the analysis and control of nonlinear dynamical systems affected by external inputs. The computation of tight comparison functions associated with this stability property is useful for assessing robustness in the iISS sense for specific systems. This paper presents a variational characterization of these tight comparison functions, along with an approach to computation via solution of an associated Hamilton-Jacobi-Bellman partial differential equation. A limiting case of relevance to the related input-to-state stability property is also considered. An illustrative example highlights the application of this approach.