Angeli, David; Sontag, Eduardo D.; Wang, Yuan A characterization of integral input-to-state stability. (English) Zbl 0979.93106 IEEE Trans. Autom. Control 45, No. 6, 1082-1097 (2000). The authors present several necessary and sufficient Lyapunov-like characterizations of the integral input-to-state stability property in terms of dissipation inequalities and a zero-detectability condition allowing the application of the LaSalle invariance principle. The notion of integral intput-to-state stability generalizes the concept of finite gain allowing to quantify sensitivity in the presence of nonlinear resonance. The paper ends with a counter-example which exhibits a forward complete and 0-GAS system which has not the integral intput-to-state stability property. Reviewer: Patrick Saint-Pierre (Paris) Cited in 140 Documents MSC: 93D25 Input-output approaches in control theory 93D05 Lyapunov and other classical stabilities (Lagrange, Poisson, \(L^p, l^p\), etc.) in control theory 93C10 Nonlinear systems in control theory Keywords:input-to-state stability; nonlinear systems; tracking; dissipation inequalities; LaSalle invariance principle PDFBibTeX XMLCite \textit{D. Angeli} et al., IEEE Trans. Autom. Control 45, No. 6, 1082--1097 (2000; Zbl 0979.93106) Full Text: DOI Link